The role of binary and ternary systems in protein studies

Authors

  • Julian Ławrynowicz Department of Solid State Physics, University of Łódź, Poland
  • Małgorzata Nowak-Kępczyk Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, Poland
  • Osamu Suzuki Department of Computer and System Analysis, College of Humanities and Sciences, Nihon University

Keywords:

binary physical structure, ternary physical structure, quaternary physical structure, quinary physical structure, senary physical structure, alloy, pentacene, polymer, protein, peptide, amino acid, Galois extension, Riemann surface

Abstract

Various aspects of binary, ternary, quaternary, quinary, and senary structures for alloys, polymers and, in particular, proteins are studied. We refer to quinary and senary structures in some polymers indicating the role of total energy maxima in the infrared and Raman activity energy spectra. Decomposition of quinary structures to ternary structures is discussed. A complex analytical method of binary and ternary Galois extension is proposed as well as its realization in terms of Riemann surfaces. Slightly wavy behaviour of the system of hexagons in a polymer leaf is investigated

References

F. Ducastelle, F. Gauthier, Generalized perturbation theory in disordered transitional alloys: Applications to the calculation of ordering energies, J. Phys. F 6 (1976), 2039; doi: 10:1088/0305-4608/6/11/065.

P. G. de Gennes, Scaling Concepts in Polymer Physics, Cornel University Press, 1979.

H. F. Gilbert, Basic Concepts in Biochemistry (A Student Survival Guide), McGraw- Hill, Inc., 1992.

J. Ławrynowicz, M. Nowak-Kępczyk, M. Zubert, Mathematics behind two related nobel prizes 2016: in physics - topology governing physics of phase transitions, in chemistry geometry of molecular nanoengines, Bull. Soc. Sci. Lettres Łódź Sér. Rech. Déform. 69 (2019), vol. 1.

J. Ławrynowicz, O. Suzuki, A. Niemczynowicz, M. Nowak-Kępczyk, Fractals and chaos related to Ising-Onsager-Zhang lattices. Ternary approach vs. binary approach, Int. J. of Geom. Meth. in Modern Physics 15, No. 11, 1850187 (2018). 01 Nov 2018, https://doi.org/10.1142/S0219887818501876 .

J. Ławrynowicz, M. Nowak-Kępczyk, A.Valianti, M. Zubert, Physics of complex alloys one dimensional relaxation problem, Bull. Soc. Sci. Lettres Łódź Sér. Rech. Déform. 65 (2015), 27–48.

J. Ławrynowicz, K. Nôno, D. Nagayama, O. Suzuki, Non-commutative Galois theory on Nonion algebra and su(3) and its application to construction of quark models, Proc. of the Annual Meeting of the Yukawa Inst. Kyoto ”The Hierarchy Structure in Physics and Information Theory” Soryuusironnkennkyuu, Yukawa Institute, Kyoto 2011, 145–157 [http://www2.yukawa.kyoto-u.ac.jp].

J. Ławrynowicz, K. Nôno, D. Nagayama, O. Suzuki, A method of non-commutative Galois theory for binary and ternary Clifford Analysis, Proc. ICMPEA (Internat. Conf. on Math. Probl. in Eng. Aerospace, and Sciences) Wien 2012, AIP (Amer. Inst. of Phys.) Conf. 1493 (2012), 1007–1014.

J. Ławrynowicz, K. Nôno, O. Suzuki, Binary and ternary Clifford analysis vs. Noncommutative Galois extensions. I. Basics of the comparison, Bull. Soc. Sci. Lettres Łódź Sér. Rech. Déform. 62 (2012), no. 1, 33–42.

R. Nevalinna, Analytic functions, Springer-Verlag, Berlin-Heidelberg-New York, 1970.

M. Nowak-Kępczyk, An algebra governing reduction of quaternary structures to ternary structures I. Reductions of quaternary structures to ternary structures, Soc. Sci. Lettres Łódź Sér. Rech. Déform. 64 (2014), no. 2, 101–109.

M. Nowak-Kępczyk, An algebra governing reduction of quaternary structures to ternary structures II. A study of the multiplication table for the resulting algebra generators, Soc. Sci. Lettres Łódź Sér. Rech. Déform. 64 (2014), no. 3, 81–90.

M. Nowak-Kępczyk, An algebra governing reduction of quaternary structures to ternary structures III. A study of generators of the resulting algebra, Soc. Sci. Lettres Łódź Sér. Rech. Déform. 66 (2016), no. 1, 123–133.

C. S.Peirce, On Nonions, in: Collected Papers of Charles Sanders Peirce, 3rd ed., vol. III, Harvard University Press, Cambridge Mass, 1967, 411–416.

O. Suzuki, The problem of Riemann-Hilbert and the relation of Fuchs in several complex variables, in: Equations Diff´erentielles et Systémes de Pfaff dans le Champ Complexe, Lecture Notes in Mathematics, Springer Verlag, 712 (1979), 325–364.

O. Suzuki, Binary and ternary structure in the evolutions of the universe (2×3×2×2 × · · · world). From space- time to molecular biology, Bull. Soc. Sci. Lettres Łódź Sér. Rech. Déform. 69 (2019), no. 1, 13–26.

O. Suzuki, Binary and ternary structure in the evolutions of the universe (2 × 3 × 2 × 2 ×· · · world) II. +The description of further stages of the evolutions (Polymers, molecular biology, and natural language), Bull. Soc. Sci. Lettres Łódź Sér. Rech. Déform. 69 (2019), no. 1, 27–34.

O. Suzuki, J. Ławrynowicz, M. Nowak-Kępczyk, M. Zubert, Some geometrical aspects of binary, ternary, quaternary, quinary and senary structures in physics, Bull. Soc. Sci. Lettres Łódź Sér. Rech. Déform. 68 (2018), no. 2, 109–122. DOI: 10.26485/0459-6854/2018/68.2/11

J. J. Sylvester, A word on nonions, John Hopkins Univ. Circulars 1 (1882), 241–242 (1883), 46; in: The Collected Mathematical Papers of James Joseph Sylvester, vol. III, Cambridge Univ. Press, Cambridge 1909, 647–650.

C. Tsallis, Introduction to nonextensive statistical mechanics (Approaching a complex world), Springer Verlag, New York, Inc. 2009.

H.Umezawa, Advanced field theory (Micro, Macro and Thermal Physics), American Institute of Physics 1993.

B. L. van der Waerden, Moderne algebra 2, Berlin Verlag von Julius Springer, 1937.

Downloads

Published

2021-08-12

Issue

Section

Articles