Boubaker Polynomials
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Contents
Definitions and recurrence relations[edit]
Boubaker polynomials are the components of a polynomial sequence ^{[1]}^{[2]}:
Boubaker polynomials are also defined in general mode through the recurrence relation:
Note that the first three polynomials are explicitly defined, and that the formula can only be used for m > 2. Another definition of Boubaker polynomials is:
Boubaker polynomials can be defined through the differential equation:
Boubaker polynomials have generated many integer sequences in the w:OnLine Encyclopedia of Integer Sequences ^{[3]} and are covered on PlanetMath.
Controversy[edit]
Several times, last time in 2009, Wikipedia chose not to host an article on the subject of Boubakr polynomials, see w:Wikipedia:Articles for deletion/Boubaker polynomials (3rd nomination). This resource is about the polynomials and applications. However, the history of Wikipedia treatment of this topic and users involved with this topic may be studied and discussed on our subpage: /Wikipedia.

 " The Boubaker polynomials were established for the first by Boubaker et al. (2006) as a guide for solving a onedimensional formulation of heat transfer equation...
 (on the domain H<x<0 and t>0) "
 " The Boubaker polynomials were established for the first by Boubaker et al. (2006) as a guide for solving a onedimensional formulation of heat transfer equation...
This is a direct quote from: Boubaker, K., "On modified Boubaker polynomials: some differential and analytical properties of the new polynomials issued from an attempt for solving bivaried heat equation," Trends in Applied Sciences Research, 2(6), 540544. [2]
This comment was appended here: "There is no 2006 reference in this article, and the reference cited as 'accepted' in 2007 cannot be found on Google Scholar."
Students who pay close attention to detail often find errors in peerreviewed publications, but such errors may also exist in interpretation. The sentence quoted above is in the cited paper by Boubaker. There is, as noted, no 2006 reference in the article, and the article is not footnoted. There are, instead, references:
 Boubaker, K., 2007. The Boubaker polynomials, a new function class for solving bivaried secondorder differential equations: F.E.J. Applied Math (Accepted).
 Boubaker, K., A. Chaouachi, M. Amlouk, and H. Bouzouita, 2007. Enhancement of pyrolysis spray disposal performance using thermal timeresponse to precursor uniform deposition. Eur. Phys. J. Applied Phys. 35: 105109.
The second source first page can be seen at [3]. The publication information given there is
 Received 9 May 2006.
 Accepted 12 October 2006.
 Published online 26 January 2007.
Since the quoted text refers to Boubaker et al, it is referring to the second reference, not the first. The second reference was accepted in 2006, and since date may have been considered important, the acceptance date was given, or even possibly the submission date. This was simply not made clear.
However, where is the first paper? It is cited in Dada et al, 2009, Establishment of a Chebyshevdependent Inhomogeneous Second Order Differential Equation for the Applied Physicsrelated BoubakerTurki Polynomials, J. Appl. Appl. Math, Vol 3 Issue 2, 329 – 336 [4], this way:
 Boubaker K. (2008). The Boubaker polynomials, a new function class for solving bivaried second order differential equations, F. E. J. of Applied Mathematics, Vol. 31, Issue 3 pp. 273436.
The paper is also cited in this 2015 "in press" publication: [5] (Boubaker is one of the authors).
The title of the paper is present on Research Gate, with more details, but the actual paper hosted there is the Applied Science paper, not the original one.[6]. This is what is shown as to the original:
 The Boubaker polynomials, A new function class for solving bivaried second order differential equations
 Karem Boubaker
 Far East Journal of Applied Mathematics 01/2008; 31(3).
 ABSTRACT This study presents new polynomials issued from an attempt to solve heat bivaried equation in a particular case of onedimensional model. The polynomials, baptized Boubaker polynomials are defined by a recursive formula, which is a critical part of resolution process; they have a demonstrated explicit forms and some interesting properties.
This is the original abstract from the publisher: [7]. It shows a received date of March 14, 2007, but was not published until June, 2008. The acceptance date is not given.
Implications of this research may be covered in analysis to be added to our subpage: /Wikipedia.
The importance of this heat equation in applied mathematics is uncontroversial, as is illustrated in the next section.
Applications[edit]
Boubaker polynomials have been used in different scientific fields:
 cryogencs^{[4]}
 biology^{[5]}
 Dynamic Systems^{[6]}
 NonLinear Systems^{[7]} ^{[8]}
 Approximation Theory^{[9]}
 Thermodynamics ^{[10]}^{[11]}^{[12]}
 mechanics ^{[13]}
 Hydrology ^{[14]}
 Molecular Dynamics ^{[15]}
 Fundamental Mathematics ^{[16]}
 Calorimetry ^{[17]}
 Biophysics ^{[18]}
 Photovoltaics ^{[19]}
 Complex Analysyis ^{[20]}
 Matrix Analysis^{[21]}
 Fundamental Physics ^{[22]}
 Applied Mathematics^{[23]}
 Cryptography^{[24]}
 Algebra^{[25]}
References[edit]
 ↑ O.D. Oyodum, O.B. Awojoyogbe, M.K. Dada, J.N. Magnuson, Eur. Phys. J. Appl. Phys. Volume 46, Number 2, May 2009, article number 21201, Comment on “Enhancement of pyrolysis spray disposal performance using thermal timeresponse to precursor uniform deposition” by K. Boubaker, A. Chaouachi, M. Amlouk and H. Bouzouita. On the earliest definition of the Boubaker polynomials", [pay wall
 ↑ Milovanovic, Gradimir V., et al. "Some properties of Boubaker polynomials and applications." AIP Conference ProceedingsAmerican Institute of Physics. Vol. 1479. No. 1. 2012. http://www.mi.sanu.ac.rs/~gvm/radovi/ASCA10501053.pdf
 ↑ oeis.org Sequences A135929, A135936 by Neil J. A. Sloane, A137276 by Roger L. Bagula and Gary Adamson, A138476 , by A. Bannour, A137289, A136256, A136255, by R. L. Bagula, A160242 by A. Rahmanov,
 ↑ citationtitle= 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
 ↑ 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 acceleratedpredatorsatiety Lotka–Volterra predator–prey problem using Boubaker polynomial expansion scheme,http://www.ncbi.nlm.nih.gov/pubmed/20109470
 ↑ Journal of Theoretical Biology (Elsevier)id=doi:10.1016/j.jtbi.2010.01.026 A. Milgeamtitle = The stability of the Boubaker polynomials expansion scheme (BPES)based solution to Lotka–Volterra problem  http://www.ncbi.nlm.nih.gov/pubmed/21145326
 ↑ Mathematical and Computer Modelling(Elsevier)iddoi:10.1016/j.mcm.2011.02.031 H. Koçak, A. Yıldırım, D.H. Zhang, S.T. MohyudDin,The Comparative Boubaker Polynomials Expansion Scheme (BPES) and Homotopy Perturbation Method (HPM) for solving a standard nonlinear secondorder boundary value problem,http://www.citeulike.org/article/8940425
 ↑ The 7th International Conference on Differential Equations and Dynamic Systems, University of South Florida, Tampa, Fmorida USA, 1518 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/Abstracts7thDEDSTampa.pdf
 ↑ Journal of Integer Sequences (JIS)Paul Barry, Aoife Hennessy,MeixnerType Results for Riordan Arrays and Associated Integer Sequences, Chapter 6: The Boubaker polynomials http://www.emis.ams.org/journals/JIS/VOL13/Barry5/barry96s.pdf
 ↑ Russian Journal of Physical Chemistry A, Focus on Chemistry (Springer) H. Koçak, Z. Dahong, A. Yildirim,A rangefree method to determine antoine vaporpressure heat transferrelated equation coefficients using the Boubaker polynomials expansion scheme http://www.springerlink.com/content/d78h761823628gl2/
 ↑ Indian Journal of Physics(Springer) H. Koçak, Z. Dahong, A. Yildirim,Analytical expression to temperaturedependent KirkwoodFröhlich dipole orientation parameter using the Boubaker Polynomials Expansion Scheme (BPES) http://www.springerlink.com/content/173787083245t267/
 ↑ Jornal of Thermophysics and Heat Transfer (American Institute of Aeronautics and Astronautics) AIAA)A. Belhadj, O. F. Onyango and N. Rozibaeva,Boubaker Polynomials Expansion SchemeRelated Heat Transfer Investigation Inside Keyhole Model http://pdf.aiaa.org/jaPreview/JTHT/2009/PVJA41850.pdf
 ↑ D.H. Zhang, "Study of a nonlinear mechanical system using Boubaker polynomials expansion scheme BPES," International Journal of NonLinear Mechanics Volume 46, Issue 2, March 2011, Pages 443–445.[1]
 ↑ Studies in Nonlinear Sciences (SNS)Emna GargouriEllouze, 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
 ↑ Journal of Structural Chemistry (Springer) W. X. Yue, H. Koçak, D. H. Zhang , A. Yıldırım,A second attempt to establish an analytical expression to steamwater dipole orientation parameter using the Boubaker polynomials expansion scheme http://www.springerlink.com/content/57681724u74gvg76/
 ↑ 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/A12zh.pdf
 ↑ Journal of Thermal Analysis and Calorimetry(Akadémiai Kiadó, Springer Science & Kluwer Academic Publishers B.V.)id=doi:10.1007/s1097300900944 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
 ↑ Heat and Mass Transfer(Springer Berlin / Heidelberg)id= Volume 45, Number 10 / août 2009, pages:12471251 doi:10.1007/s002310090493x S. Amir Hossein A. E. Tabatabaei, T. Gang Z., O. Bamidele A. and Folorunsho O. Moses,Cutoff 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/
 ↑ Modern Physics Letters B ([ISSN: 02179849, by WS: World Scientific Publishing Co Pte Ltd] )S. Fridjine and M. Amlouk,A NEW PARAMETERABACUS FOR OTIMIZING PVT HYBRID SOLAR DEVICES FUNCTIONAL MATERIALS USING BOUBAKER POLYNOMIALS EXPANSION SCHEME http://www.worldscinet.com/mplb/23/2317/S0217984909020321.html
 ↑ citation T. G. Zhao, Y. X. Wang and K. B. Ben Mahmoud title=Limit and uniqueness of the BoubakerZhao polynomials single imaginary root sequence  journal=International Journal of Mathematics and Computation  volume=1 number=08  ISSN=09745718  http://ceser.res.in/ijmc.html
 ↑ A. Luzon , M.  last2=Moron   title=RECURRENCE RELATIONS FOR POLYNOMIAL SEQUENCES VIA RIORDAN MATRICES, Pages 2425: BOUBAKER POLYNOMIALS associated Riordan matrix  http://arxiv.org/PS_cache/arxiv/pdf/0904/0904.2672v1.pdf
 ↑ M. Agida , A. S. .  last2=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
 ↑ A. S. Kumar , An analytical solution to applied mathematicsrelated 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
 ↑ 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
 ↑ Kiliç Bülent, Erdal Bas, Page 7, Citation 27: Boubaker polynomials , http://cujse.cankaya.edu.tr/archive/14/02_cujse_10018.pdf
Sources[edit]
Subpage for the collection of sources on Boubaker polynomials: /Sources
Resources[edit]
 Boubaker Polynomials

 /Wikipedia study of Wikipedia history re this topic

 /Wikipedia/en.wp AfD 2 study of the second Wikipedia Articles for deletion discussion
 /Wikipedia/en.wp AfD 3 study of the third Wikipedia Articles for deletion discussion
 /Wikipedia/Chebyshev study of attempts to edit w:Chebyshev polynomials to mention BPs
 /Wikipedia/Deletion review study of a Deletion review on Boubaker polynomials
 /Wikipedia/SPI study of users involved, accused of being socks of Boubaker, beginning with Sock Puppet Investigations
 /Wikipedia/White Fennec holds former White Fennec user pages, useful for study of history
 /Sources list of peerreviewed sources categorized as having Boubaker as author or coauthor

 /Sources/by date List of peerreviewed sources organized by year of publication
 /Essays and student notes
 /Boubaker ... about the professor.