najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2020-11-1-36-43najo-465Research ArticlePHYSICSФИЗИКАGeometrical analyses of nanostructuresSajfertV.

Djure Djakovica Street bb, 23000 Zrenjanin

PopN.

V. Parvan. No.2, 300223, Timisoara

nicolina.pop@upt.roPopovD.

V. Parvan. No.2, 300223, Timisoara

Technical Faculty “Mihajlo Pupin” ZrenjaninSerbiaDepartment of Physical Foundations of Engineering, Politehnica University of Timis¸oaraRomania20203107202511136–43Copyright © Sajfert V., Pop N., Popov D., 20252025Sajfert V., Pop N., Popov D.Sajfert V., Pop N., Popov D.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/465

In this paper, the statistical and dynamical equivalence between rectangular cell and lower symmetry cell is presented. The achievement of this equivalence will improve theoretical investigations of nanostructures as thin film or quantum rods.

Nanostructurestriclinic cellcubic cellthin filmThis work was supported by a grant of the Romanian Ministry of Research and Innovation, project number 10PFE/16.10.2018, PERFORM-TECH-UPT – The increasing of the institutional performance of the Polytechnic University of Timis¸oara by strengthening the research, development and technological transfer capacity in the field of “Energy, Environment and Climate Change”, within Program 1 – Development of the national system of Research and Development, Subprogram 1.2 – Institutional Performance – Institutional Development Projects – Excellence Funding Projects in RDI, PNCDI III.ReferencesKittel Ch. Introduction to Soild State Physics, 7th ed., New York, Wiley, 1995.Kittel Ch. Introduction to Soild State Physics, 7th ed., New York, Wiley, 1995.Siegel R.W., Hu E., Roko M.C. (eds.) Nanostructure Science and Technology A Worldwide Study Prepared under the guidance of the IWGN, NSTC, WTEC, Loyola College in Maryland, 2004, URL: http://www.whitehouse.gov/WH/EOP/OSTP/NSTC.Siegel R.W., Hu E., Roko M.C. (eds.) Nanostructure Science and Technology A Worldwide Study Prepared under the guidance of the IWGN, NSTC, WTEC, Loyola College in Maryland, 2004, URL: http://www.whitehouse.gov/WH/EOP/OSTP/NSTC.Sajfert V.,¯Dajic R.,´ Cetkovi´ c M., To´ siˇ c B. Cylindrical quantum dots with hydrogen-boned materials.´ Nanotoechnology, 2003, 14, P. 358–365.Sajfert V.,¯Dajic R.,´ Cetkovi´ c M., To´ siˇ c B. Cylindrical quantum dots with hydrogen-boned materials.´ Nanotoechnology, 2003, 14, P. 358–365.Sajfert V., ¯Dajic R., To´ siˇ c B.S., Hydrogen-Bonded Nanotubes as a Model for DNA Transcription.´ J. Nanosci. Nanotech., 2004, 4 (7), P. 886– 890 .Sajfert V., ¯Dajic R., To´ siˇ c B.S., Hydrogen-Bonded Nanotubes as a Model for DNA Transcription.´ J. Nanosci. Nanotech., 2004, 4 (7), P. 886– 890 .Sajfert V., Setrajˇ ciˇ c J., To´ siˇ c B.,´ ¯Dajic R. Excitonic Diffusion in Thin Molecular films.´ Czechoslovak Journal of Physics, 2004, 54 (9), P. 975– 988.Sajfert V., Setrajˇ ciˇ c J., To´ siˇ c B.,´ ¯Dajic R. Excitonic Diffusion in Thin Molecular films.´ Czechoslovak Journal of Physics, 2004, 54 (9), P. 975– 988.Sajfert V., Tosiˇ c B. Conductance Properties of Cylindrical Quantum Nano Dots.´ Journal of Computational and Theoretical Nanoscience, 2005, 2 (1) P. 148–153.Sajfert V., Tosiˇ c B. Conductance Properties of Cylindrical Quantum Nano Dots.´ Journal of Computational and Theoretical Nanoscience, 2005, 2 (1) P. 148–153.Sajfert V., Setrajˇ ciˇ c J.P., Ja´ cimovski S., To´ siˇ c B. Thermodynamic and Kinetic Properties of Cylindrical Quantum dots.´ Physica E: Lowdimensional Systems and Nanostructures, 2005, 25 (4), P. 479–491.Sajfert V., Setrajˇ ciˇ c J.P., Ja´ cimovski S., To´ siˇ c B. Thermodynamic and Kinetic Properties of Cylindrical Quantum dots.´ Physica E: Lowdimensional Systems and Nanostructures, 2005, 25 (4), P. 479–491.Backovic D., Sajfert V.,´ Setrajˇ ciˇ c J., To´ siˇ c B. Magnetic Nanorod in the Transition Temperature Vicinity.´ Journal of Computational and Theoretical Nanoscience, 2005, 2 (3), P. 448–455.Backovic D., Sajfert V.,´ Setrajˇ ciˇ c J., To´ siˇ c B. Magnetic Nanorod in the Transition Temperature Vicinity.´ Journal of Computational and Theoretical Nanoscience, 2005, 2 (3), P. 448–455.Popov D., Dong S.H., et al. Construction of the Barut-Girardello quasi coherent states for the Morse potential. Annals of Physics, 2013, 339, P. 122–134.Popov D., Dong S.H., et al. Construction of the Barut-Girardello quasi coherent states for the Morse potential. Annals of Physics, 2013, 339, P. 122–134.Smolkina M.O., Popov I.Y. , Blinova I.V., Milakis E. On the metric graph model for flows in tubular nanostructures. Nanosystems: Physics, Chemistry, Mathematics, 2019, 10 (1), P. 6–11.Smolkina M.O., Popov I.Y. , Blinova I.V., Milakis E. On the metric graph model for flows in tubular nanostructures. Nanosystems: Physics, Chemistry, Mathematics, 2019, 10 (1), P. 6–11.Ziman J.M. Principles of the Theory of Solids, Cambridge University Press, 1972.Ziman J.M. Principles of the Theory of Solids, Cambridge University Press, 1972.Puta M., Iacob F. Geometric prequantization of the symmetric rigid body. Differential Geometry and Its Applications, 2001, 39, P. 385–390.Puta M., Iacob F. Geometric prequantization of the symmetric rigid body. Differential Geometry and Its Applications, 2001, 39, P. 385–390.Ibach H., Luth H.¨ SolidState Physis, An Introduction to Principles of Material Science, 3rd edition, Springer-Verlag, Berlin, Heidelberg, New York, 2003.Ibach H., Luth H.¨ SolidState Physis, An Introduction to Principles of Material Science, 3rd edition, Springer-Verlag, Berlin, Heidelberg, New York, 2003.Zubarev D. Statistical Mechanics of Nonequilibrium Processes, Basic Concepts, Kinetic Theory, Wiley, New York, 1997.Zubarev D. Statistical Mechanics of Nonequilibrium Processes, Basic Concepts, Kinetic Theory, Wiley, New York, 1997.Chaikin P.B., Lubensky T.C. Principles of Condensed Matter Physics, Cambridge University Press, 1995.Chaikin P.B., Lubensky T.C. Principles of Condensed Matter Physics, Cambridge University Press, 1995.yablikov S.V. Methods in the Quantum Theory in Magnetism, Plenum Press, New York, 1967.yablikov S.V. Methods in the Quantum Theory in Magnetism, Plenum Press, New York, 1967.Gradshteyn I.S., Ryzhik I.M. Table of Integrals, Series, and Products, Academic Press, New York, London, 1965.Gradshteyn I.S., Ryzhik I.M. Table of Integrals, Series, and Products, Academic Press, New York, London, 1965.Sajfert V., Bucalovic N., Ma´ skoviˇ c Lj., To´ siˇ c B. Electrons in thin films.´ Czechoslovak Journal of Physics, 2006, 56, P. 253–266.Sajfert V., Bucalovic N., Ma´ skoviˇ c Lj., To´ siˇ c B. Electrons in thin films.´ Czechoslovak Journal of Physics, 2006, 56, P. 253–266.

The authors declare that there are no conflicts of interest present.