ROLA SYSTEMÓW BINARNYCH I TERNARNYCH W BADANIU BIAŁEK
Słowa kluczowe:
binarna struktura fizyczna, ternarna struktura fizyczna, kwaternarna struktura fizyczna, kwinarna struktura fizyczna, sennarna struktura fizyczna, stop, pentacen, polimer, białko, peptyd, aminokwas, rozszerzenie Galois, powierzchnia RiemannaAbstrakt
Rozważamy rozmaite aspekty struktur binarnych, ternarnych, kwaternarnych i senarnych dla stopów, polimerów i protein. W szczególności odnosimy się do struktur kwinarnych i senarnych w niektórych polimerach wskazując na rolę maksimów energii w spektrach podczerwieni i aktywności Ramana. Dyskutujemy rozkład struktur kwinarnych do ternarnych. Proponujemy zespoloną metodę analityczną dla binarnych i ternarnych rozszerzeń Galois, jak również ich realizację na powierzchniach Riemanna. Omawiamy lekko falujące zachowanie układu sześciokątów w liściu polimeru
Bibliografia
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.
