Identyfikatory
Warianty tytułu
Spira Mirabilis w wybranych modelach rachunku operatorów Bittnera
Języki publikacji
Abstrakty
Parametric descriptions of spirals being analogues of the logarithmic spiral are determined using the concept of the exponential element in the non-classical Bittner operational calculus and applying the chosen models of it.
Korzystając z pojęcia elementu wykładniczego w nieklasycznym rachunku operatorów Bittnera oraz stosując wybrane modele tego rachunku, wyznaczono opisy parametryczne spiral będących odpowiednikami spirali logarytmicznej.
Czasopismo
Rocznik
Tom
Strony
65--96
Opis fizyczny
Bibliogr. 32 poz., rys., tab.
Twórcy
autor
- Polish Naval Academy, Faculty of Mechanical and Electrical Engineering , Śmidowicza 69 Str., 81 - 127 Gdynia, Poland
Bibliografia
- [1] Bellert S., Prace wybrane: wydanie pośmiertne, PWN, Warszawa — Wrocław 1980 [Selected Papers: Posthumous Edition — available in Polish].
- [2] Bittner R., Algebraic and analytic properties of solutions of abstract differential equations,‘Rozprawy Matematyczne’ [‘Dissertationes Math.’], 41, PWN, Warszawa 1964.
- [3] Bittner R., Operational calculus in linear spaces, ‘Studia Math.’, 1961, 20, pp. 1–18.
- [4] Bittner R., Rachunek operatorów w przestrzeniach liniowych, PWN, Warszawa 1974 [Operational Calculus in Linear Spaces — available in Polish].
- [5] Borodin A. I., Bugaj A. S., Biografičeskij slovar’ dejatelej v oblasti matematiki, Radjans’ka Škola, Kiev 1979 [Biographical Dictionary of Activists in the Field of Mathematics — availablein Russian].
- [6] Boyer C. B., The History of the Calculus and its Conceptual Development, Dover Publ., Inc., New York 1949.
- [7] Caruso H. A., Marotta S. M., Sequences of complex numbers resembling the Fibonacci series, ‘Revista Ciências Exatas e Naturais’, 2000, 2(1), pp. 49–59.
- [8] Dimovski I. H., Kiryakova V. S., Discrete operational calculi for two-sided sequences, ‘The Fibonacci Quarterly’ (Proc. 5th Internat. Conf. on Fibonacci Numbers and Their Applications), 1993, 5, pp. 159–168.
- [9] Ditkin V. A., Prudnikov A. P., Integral’nye preobrazovaniâ i operacionnoe isčislenie, Nauka, Moskva 1974 [Integral Transforms and Operational Calculus — available in Russian]
- [10] Do Carmo M. P., Differential Geometry of Curves and Surfaces, Prentice-Hall, New Jersey 1976.
- [11] Embree M., Trefethen L. N., Growth and decay of random Fibonacci sequences, ‘Proceedings: Mathematical, Physical and Engineering Sciences’, 1987, 455 (Jul. 8, 1999), The Royal Society, pp. 2471–2485.
- [12] Falcón S., Plaza A., On the Fibonacci k-numbers, ‘Chaos, Solitons and Fractals’, 2007, 32(5), pp. 1615–1624.
- [13] Fishburn P. C., Odlyzko A. M., Roberts F. S., Two-sided generalized Fibonacci sequences, ‘The Fibonacci Quarterly’, 1989, 27, 352–361.
- [14] Gazalé M. J., Gnomon: From Pharaohs to Fractals, Princeton Univ. Press, New Jersey 1999.
- [15] Gdowski B., Elementy geometrii różniczkowej z zadaniami, PWN, Warszawa 1982 [Elements of Differential Geometry with Exercises — available in Polish].
- [16] Hambidge J., Dynamic Symmetry: The Greek Vase, Yale Univ. Press, New Haven 1920.
- [17] Hayes B., The Vibonacci numbers, ‘American Scientist’, 1999, 87(4), pp. 296–301.
- [18] http://functions.wolfram.com/03.02.02.0001.01 [access 27.06.2015].
- [19] http://functions.wolfram.com/07.18.02.0001.01 [access 27.06.2015].
- [20] Knuth D. E., NegaFibonacci numbers and the hyperbolic plane, The ‘Pi Mu Epsilon J. Suth-erland Frame’ memorial lecture at ‘MathFest 2007’ in San José, CA, 2007-08-04, http://www.pme-math.org/conferences/national/2007/2007.html [access 29.06.2015].
- [21] Koshy T., Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, Inc., New York 2001.
- [22] Livio M., Golden Ratio — The Story of Phi, the World’s Most Astonishing Number, Broadway Books, New York 2002.
- [23] Mikusiński J., Operational Calculus, Pergamon Press, New York 1959.
- [24] Posmantier A. S., Lehmann I., The Fabulous Fibonacci Numbers, Prometheus Books, Amherst, New York 2007.
- [25] Przeworska-Rolewicz D., Algebraic Analysis, D. Reidel & PWN, Dordrecht, Warszawa 1988.
- [26] Spinadel V. W., New Smarandache Sequences: The Family of Metallic Means, [online], http://vixra.org/abs/1403.0507 [access 29.06.2015].
- [27] Spinadel V. W., The Family of Metallic Means, ‘VisMath — Visual Mathematics’, Electronic Journal, 1999, Vol. 1(3), [online], http://www.mi.sanu.ac.rs/vismath/spinadel/index.html [access 29.06.2015].
- [28] Stakhov A., The Mathematics of Harmony: From Euclid to Contemporary Ma-thematics and Computer Science, Series of Knots and Everything, Vol. 22, World Scientific, Singapore 2009.
- [29] Thompson D. W., On Growth and Form, Cambridge Univ. Press, The Macmillian Comp., New York 1945.
- [30] Viswanath D., Random Fibonacci sequences and the number 1.13198824..., ‘Mathematics of Computation’, 1999, 69(231), pp. 1131–1155.
- [31] Wysocki H., Model nieklasycznego rachunku operatorów Bittnera dla różnicy wstecznej, ‘Ze-szyty Naukowe Akademii Marynarki Wojennej’, 2010, 2(181), pp. 37–48 [Bittner non-classical operational calculus model for the backward difference — available in Polish].
- [32] Wysocki H., Rozwiązanie liniowego równania różnicowego w przestrzeni wyników genero-wanej przez ciągi dwustronne, ‘Zeszyty Naukowe Akademii Marynarki Wojennej’, 2010, 3(182), pp. 85–101 [The solution of a linear difference equation in the space of results gene-rated by two-sided sequences — available in Polish].
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-db51a130-3d3c-4a79-b8f9-c4a041a0276a