Polinomi di Boubaker

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Polinomi di Boubaker
Tipo di risorsa Tipo: lezione
Materia di appartenenza Materia: Algebra

I polinomi di Boubaker sono le componenti di una successione polinomiale che inizia con i seguenti polinomi[1]:

I polinomi di Boubaker possono essere definiti in modo generalizzato tramite la formula:

Un'altra possibile definizione di questi polinomi è la seguente:

Alternativamente, i polinomi di Boubaker possono essere definiti tramite l'equazione differenziale:

I polinomi di Boubaker hanno prodotto molte sequenze nell'Enciclopedia On-line di Sequenze di Numeri Interi' (OEIS) On-Line Encyclopedia of Integer Sequences[2] e PlanetMath.


I polinomi di Boubaker sono ampiamente utilizzati nei seguenti ambiti:


  1. O.D. Oyodum, O.B. Awojoyogbe, M.K. Dada, J.N. Magnuson, Eur. Phys. J. Appl. Phys. Volume 46, pages 2120-21202, On the earliest definition of the Boubaker polynomials , [1]
  2. Sequences A135929 and A135936 by Neil J. A. Sloane, A137276 by Roger L. Bagula and Gary Adamson, A138476 by A. Bannour, A137289, A136256, and A136255 by R. L. Bagula at the On-Line Encyclopedia of Integer Sequences
  3. Book:Cryogenics: Theory, Processes and Applications, Chapter 8: Cryogenics Vessels Thermal Profilng Using the Boubaker Polynomials Expansion Scheme Investigation , Editor: Allyson E.Hayes https://www.novapublishers.com/catalog/product_info.php?products_id=17332&osCsid=06f25d4f739dc8ec36c5160f480acaef
  4. Journal of Theoretical Biology (Elsevier)|id=doi:10.1016/j.jtbi.2010.12.002 B. Dubey, T.G. Zhao, M. Jonsson, H. Rahmanov,A solution to the accelerated-predator-satiety Lotka–Volterra predator–prey problem using Boubaker polynomial expansion scheme,http://www.ncbi.nlm.nih.gov/pubmed/20109470
  5. Journal of Theoretical Biology (Elsevier)|id=doi:10.1016/j.jtbi.2010.01.026 A. Milgeam|title = The stability of the Boubaker polynomials expansion scheme (BPES)-based solution to Lotka–Volterra problem | http://www.ncbi.nlm.nih.gov/pubmed/21145326
  6. Mathematical and Computer Modelling(Elsevier)|iddoi:10.1016/j.mcm.2011.02.031 H. Koçak, A. Yıldırım, D.H. Zhang, S.T. Mohyud-Din,The Comparative Boubaker Polynomials Expansion Scheme (BPES) and Homotopy Perturbation Method (HPM) for solving a standard nonlinear second-order boundary value problem,http://www.citeulike.org/article/8940425
  7. The 7th International Conference on Differential Equations and Dynamic Systems, University of South Florida, Tampa, Fmorida USA, 15-18 December 2010 <Page 40 > A. Yildirim,The boubaker polynomials expansion scheme for solving nonlinear science problems, http://web3.cas.usf.edu/main/depts/mth/7thde/data/Abstracts-7thDEDS-Tampa.pdf
  8. Journal of Integer Sequences (JIS)Paul Barry, Aoife Hennessy,Meixner-Type Results for Riordan Arrays and Associated Integer Sequences, Chapter 6: The Boubaker polynomials http://www.emis.ams.org/journals/JIS/VOL13/Barry5/barry96s.pdf
  9. Russian Journal of Physical Chemistry A, Focus on Chemistry (Springer) H. Koçak, Z. Dahong, A. Yildirim,A range-free method to determine antoine vapor-pressure heat transfer-related equation coefficients using the Boubaker polynomials expansion scheme http://www.springerlink.com/content/d78h761823628gl2/
  10. Indian Journal of Physics(Springer) H. Koçak, Z. Dahong, A. Yildirim,Analytical expression to temperature-dependent Kirkwood-Fröhlich dipole orientation parameter using the Boubaker Polynomials Expansion Scheme (BPES) http://www.springerlink.com/content/173787083245t267/
  11. Jornal of Thermophysics and Heat Transfer (American Institute of Aeronautics and Astronautics) AIAA)A. Belhadj, O. F. Onyango and N. Rozibaeva,Boubaker Polynomials Expansion Scheme-Related Heat Transfer Investigation Inside Keyhole Model| http://pdf.aiaa.org/jaPreview/JTHT/2009/PVJA41850.pdf
  12. International Journal of Non-Linear Mechanics (NASA Astrophysics Data System) D. H. Zhang,Study of a non-linear mechanical system using Boubaker polynomials expansion scheme BPES http://adsabs.harvard.edu/abs/2011IJNLM..46..443Z
  13. Studies in Nonlinear Sciences (SNS)Emna Gargouri-Ellouze, Noreen Sher Akbar, Sohail Nadeem,Modelling Nonlinear Bivariate Dependence Using the Boubaker Polynomials Copula The Boubaker polynomials http://idosi.org/sns/2(1)11/3.pdf
  14. Journal of Structural Chemistry (Springer) W. X. Yue, H. Koçak, D. H. Zhang , A. Yıldırım,A second attempt to establish an analytical expression to steam-water dipole orientation parameter using the Boubaker polynomials expansion scheme http://www.springerlink.com/content/57681724u74gvg76/
  15. Applied Sciences,(Balkan Society of Geometers, Geometry Balkan Press) D. H. Zhang, L. Naing,The Boubaker polynomials expansion scheme BPES for solving a standard boundary value problem http://www.mathem.pub.ro/apps/v12/A12-zh.pdf
  16. Journal of Thermal Analysis and Calorimetry(Akadémiai Kiadó, Springer Science & Kluwer Academic Publishers B.V.)|id=doi:10.1007/s10973-009-0094-4 A. Belhadj, J. Bessrour, M. Bouhafs and L. Barrallier,Experimental and theoretical cooling velocity profile inside laser welded metals using keyhole approximation and Boubaker polynomials expansion| http://www.springerlink.com/content/2l03064124057686/?p=15de2fa57ce5478aa8a62c2b3a618213&pi=1
  17. Heat and Mass Transfer(Springer Berlin / Heidelberg)|id= Volume 45, Number 10 / août 2009, pages:1247-1251 doi:10.1007/s00231-009-0493-x S. Amir Hossein A. E. Tabatabaei, T. Gang Z., O. Bamidele A. and Folorunsho O. Moses,Cut-off cooling velocity profiling inside a keyhole model using the Boubaker polynomials expansion scheme| http://www.citeulike.org/article/4834321 | http://www.springerlink.com/content/b125h6166r216313/
  18. Modern Physics Letters B ([ISSN: 0217-9849, by WS: World Scientific Publishing Co Pte Ltd] )S. Fridjine and M. Amlouk,A NEW PARAMETER-ABACUS FOR OTIMIZING PV-T HYBRID SOLAR DEVICES FUNCTIONAL MATERIALS USING BOUBAKER POLYNOMIALS EXPANSION SCHEME| http://www.worldscinet.com/mplb/23/2317/S0217984909020321.html
  19. citation T. G. Zhao, Y. X. Wang and K. B. Ben Mahmoud| title=Limit and uniqueness of the Boubaker-Zhao polynomials single imaginary root sequence | journal=International Journal of Mathematics and Computation | volume=1 |number=08 | ISSN=0974-5718 | http://ceser.res.in/ijmc.html
  20. A. Luzon , M. Moron | | title=RECURRENCE RELATIONS FOR POLYNOMIAL SEQUENCES VIA RIORDAN MATRICES, Pages 24-25: BOUBAKER POLYNOMIALS associated Riordan matrix | http://arxiv.org/PS_cache/arxiv/pdf/0904/0904.2672v1.pdf
  21. M. Agida , A. S. . =Kumar |title=A Boubaker Polynomials Expansion Scheme Solution to Random Love's Equation in the Case of a Rational Kernel || journal=El. Journal of theretical physics ( EJTP) | http://www.ejtp.com/articles/ejtpv7i24p319.pdf
  22. A. S. Kumar , An analytical solution to applied mathematics-related Love's equation using the ‘''Boubaker polynomials''' expansion scheme| journal=International Journal of the Franklin Institute (elsevier) | http://cat.inist.fr/?aModele=afficheN&cpsidt=23388093
  23. B. Tirimula Rao, P. Srinivsu, C. Anantha Rao, K. Satya Vivek Vardhan , Jami Vidyadhari ,Page 8 : Boubaker polynomials ,http://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1523651_code1403499.pdf?abstractid=1523651&mirid=3
  24. Kiliç Bülent, Erdal Bas, Page 7, Citation 27: Boubaker polynomials , http://cujse.cankaya.edu.tr/archive/14/02_cujse_10018.pdf


  • Encyclopedia of Physics Research
Encyclopedia of Physics Research, Chapter 21: Cryogenics Vessels Thermal Profilng Using the Boubaker Polynomials, Editors: Nancy B. Devins and Jillian P. Ramos [2]
  • NASA: USA-Physics Abstract Service Database
a New Parameter:. AN Abacus for Optimizing Pv-T Hybrid Solar Device Functional Materials Using the Boubaker Polynomials Expansion Scheme and citation|title= http://adsabs.harvard.edu/cgi-bin/nph-data_query?doi=10.1007/s00231-009-0493-x&db_key=PHY&link_type=ABSTRACT&high=499df58f2b32224
De Khawarizmi à Euler, La Presse Magazine|date=January 9, 2008 fr, vedi anche tunisie7arts.com
Le polynôme de Boubaker|journal=La Presse Magazine|date=April 22, 2007|issue=1019|page=6 [3]
A new polynomial sequence... The Boubaker Polynomials|journal=Numerical Methods for Partial Differential Equations NMPDE [4]
Solution to Heat Equation Using Boubaker Polynomials|journal=J. of Thermophysics and Heat Transfer [5]
Boubaker Polynomials Weak Solutions to a Robin Boundary Conditioned Dynamic-State Heat Transfer Problem |journal=International Journal of Heat Transfer [6]
  • WS World Scientific Publishing Co Pte Ltd
  • Pubblicazioni accademiche
A new polynomial sequence ...The Boubaker Polynomials, International Journal of Applied Mathematics [8]
  • ENEA Ente Nazionale per le Energie Alternative
citation|title=An attempt... using Boubaker Polynomials|journal= International Journal of Heat and Technology [23]
citation|title=Numerical Distribution of Temperature During Welding Using Boubaker Polynomials , Numerical Heat Transfer, Part A, Applications [24]
Establishment of an Ordinary Generating Function and a Christoffel-Darboux Type First-Order Differential Equation for the Heat Equation Related Boubaker-Turki Polynomials, Journal of Differential Equations and C.P. [25]
Some new properties of the applied-physics related Boubaker polynomials [26]
citation 3, Page 97 C.P., [27]
Meixner-type results for Riordan arrays and associated integer sequences, Chap. 6 Boubaker Polynomials
An analytical solution to applied mathematics-related Love's equation using the Boubaker polynomials expansion scheme
Some new features of the Boubaker polynomials expansion scheme
The Boubaker polynomials expansion scheme BPES for solving a standard boundary value problem