User:White Fennec/New version 2011
Contents
 1 Boubaker Polynomials
 2 Integer Sequences generated by the Boubaker polynomials”
 3 Fields of applications
 3.1 Cryogenics
 3.2 Biology and Biophysics
 3.3 Dynamic Systems
 3.4 NonLinear Systems
 3.5 Approximation Theory
 3.6 Thermodynamics and Calorimetry
 3.7 Mechanics and Hydrology
 3.8 Molecular Dynamics
 3.9 Fundamental Mathematics and Fundamental Physics
 3.10 Photovoltaics
 3.11 Algebra, Complex Analysyis, Matrix Analysis and Cryptography
 4 References
 5 External links
Boubaker Polynomials[edit]
According to P. Barry et al.^{[1]}, A. Kumar^{[2]} and N. B. Devins et al. (in the Encyclopedia of Physics Research) ^{[3]}, The Boubaker polynomials are the components of a polynomial sequence ^{[4]}:
The Boubaker polynomials are also defined in general mode through the formula:
The Boubaker polynomials are also be defined through the differential equation:
Integer Sequences generated by the Boubaker polynomials”[edit]
The Boubaker polynomials have generated many integer sequences in the OnLine Encyclopedia of Integer Sequences (OEIS)^{[5]}:
 A131386 and A167375 by J. Ghanouchi and J. Mathar.
 A135929 , A135936 by Neil J. A. Sloane.
 A136160, A136255, A136256, A137277 and A137289 by R. L. Bagula
 A137276 by Roger L. Bagula and Gary Adamson.
 A138476, by A. Bannour.
 A160242 by Haidar Rahmanov.
 A161718 by M. Amlouk.
 A162180 by Haidar Rahmanov., N. J. A. Sloane and Joerg Arndt
 A167373, A167543 and A167387 by J. Ghanouchi .
 A172254 by L. Naing.
 A167541 by J. Ghanouchi, J. Mathar and N. J. A. Sloane.
 A167544 by J. Ghanouchi, J. Mathar and Vincenzo Librandi .
 A192011 by Paul Curtz and Johannes W. Meijer.
Fields of applications[edit]
The Boubaker polynomials have been widely used in different scientific fields:
Cryogenics[edit]
Heat equation inside lowtemperatures vessels has been solved using the Boubaker Polynomials Expansion Scheme BPES. The results published by Allyson E. Hayes represent reliable and exploitable temperature profiles between 252°C and 233°C ^{[6]} ^{[7]}.
Biology and Biophysics[edit]
The works of B. Dubey et al. ^{[8]} provided analytical solutions to the wellknown LotkaVolterra PredatorPrey equations in the case of quickly satiable predators. The model incorporated an original acceleratedpredatorsatiety function which is claimed to be closer to reality, and used the Boubaker Polynomials Expansion Scheme BPES. Thanks to this model, it has been demonstrated that, oppositely to most of the predatorpray problem scenarios predation is not strictly proportional to the prey density in presence predators which are ‘never not hungry’.
Dynamic Systems[edit]
A. Milgram used the Boubaker Polynomials Expansion Scheme BPES in order to discuss the stability of some dynamic systems ^{[9]}.
NonLinear Systems[edit]
NonLinear Systems have been also subjected to Comparative Boubaker Polynomials Expansion Scheme (BPES) and Homotopy Perturbation Method (HPM) analysis by H. Koçak et al.^{[10]} and A. Yildirim ^{[11]}
Approximation Theory[edit]
Paul Barry and Aoife Hennessy outlined the role of the Boubaker polynomials and their associated integer sequences in arrays analysis and approximation theory ^{[12]}
Thermodynamics and Calorimetry[edit]
In the field of thermodynamics and calorimetry, H. Koçak used the Boubaker Polynomials Expansion Scheme BPES in order to determine the coefficients of Antoine vaporpressure equation coefficients ^{[13]}, as well as an analytical expression to temperaturedependent KirkwoodFröhlich dipole orientation parameter ^{[14]}. In the same context, A. Belhadj et al. performed accurate thermal profiles inside Laser keyholes using the same scheme ^{[15]}^{[16]}
Mechanics and Hydrology[edit]
NASA Astrophysics Data System published a study on NonLinear Mechanics, carried out by D. H. Zhang , who used the Boubaker Polynomials Expansion Scheme (BPES) for identification of a nonlinear 2degreeoffreedom mechanical system. Thanks to these polynomials, differential equations governing mechanical system behaviours have been transformed into algebraic equations and solutions were plotted in the frequency–energy plane.^{[17]}. Similarly, E. G. Ellouze et al. established the Boubaker Polynomials Copula as a tool for solving hydrological bivariate problems ^{[18]}. E. G. Ellouze et al. applied the Boubaker Polynomials copula to a set of discrete random vectors possessing uniform margins. They further suggested a pragmatic way to fit the dependence structure of multivariate data to Boubaker Polynomials copula and empirical contingency tables, and finally established applications of the relationship between infiltration index and the average intensity of rainfall event in some zones.
Molecular Dynamics[edit]
In the field of molecularscale dynamics, W. X. Yue et al. evaluated water molecule dipole orientation parameters ^{[19]} using the Boubaker Polynomials
Fundamental Mathematics and Fundamental Physics [edit]
The Boubaker Polynomials have been used in fundamental mathematics as tools for solving some standard boundary value problems. ) D. H. Zhang et al. ^{[20]} proposed an analytical solution to well known appliedphysicsrelated KleinGordon equation. Trough some examples, D. H. Zhang et al. presented good fundaments to the Boubaker Polynomials Expansion Scheme BPES , particularly when exact solutions expressions were difficult to establish. In fundamental Physics, works of M. Agida et al. have also used the Boubaker Polynomials Expansion Scheme BPES in order to find exact analytical, piecewise continuous and differentiable solutions to Love’s equation^{[21]},
Photovoltaics[edit]
Boubaker polynomials have been applied in the domain of material characterization. Fridjine et al. Use these polynomials differential equation and algebraic equation in order to investigate Photovoltaicthermal hybrid solar cells materials^{[22]}
Algebra, Complex Analysyis, Matrix Analysis and Cryptography[edit]
The contribution of the Boubaker polynomials ^{[23]} in Pure and applied algebra can be seen through the publications of A. Lzon et al. ^{[24]}, S. Kumar ^{[25]} K. Bülent et al. ^{[26]}, C. R. Caldera et al. ^{[27]} ^{[28]} and B. T. Rao et al. ^{[29]}
References[edit]
 ↑ Paul Barry and Aoife Hennessy, Journal of Integer Sequences (JIS),MeixnerType Results for Riordan Arrays and Associated Integer Sequences, Chapter 6: The Boubaker polynomials [1]
 ↑ 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) [2]
 ↑ Encyclopedia of Physics Research, Chapter 21: Cryogenics Vessels Thermal Profilng Using the Boubaker Polynomials, Editors: Nancy B. Devins and Jillian P. Ramos, [3]
 ↑ O.D. Oyodum, O.B. Awojoyogbe, M.K. Dada, J.N. Magnuson, Eur. Phys. J. Appl. Phys. Volume 46, pages 212021202, On the earliest definition of the Boubaker polynomials , [4]
 ↑ OnLine Encyclopedia of Integer Sequences
 ↑ citationtitle= Book:Cryogenics: Theory, Processes and Applications, Chapter 8: Cryogenics Vessels Thermal Profilng Using the Boubaker Polynomials Expansion Scheme Investigation , Editor: Allyson E.Hayes [5]
 ↑ Satomi Matsumoto and Ueda Iwate, Book:Materials Science Researcher Biographical Sketches and Research Summaries, Cryogenics Vessels Thermal Profilng Using the Boubaker Polynomials Expansion Scheme Investigation,Chapter: Cryogenics Vessels Thermal Profilng Using the Boubaker Polynomials Expansion Scheme Investigation
 ↑ 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, [6]
 ↑ Journal of Theoretical Biology (Elsevier)id=doi:10.1016/j.jtbi.2010.01.026 A. Milgramtitle = The stability of the Boubaker polynomials expansion scheme (BPES)based solution to LotkaVolterra problem  [7]
 ↑ 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 [8]
 ↑ 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 [9]
 ↑ 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/
 ↑ Journal 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 [10]
 ↑ 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 [11]
 ↑ International Journal of NonLinear Mechanics (NASA Astrophysics Data System) D. H. Zhang,Study of a nonlinear mechanical system using Boubaker polynomials expansion scheme BPES [12]
 ↑ Studies in Nonlinear Sciences (SNS)Emna GargouriEllouze, Noreen Sher Akbar, Sohail Nadeem,Modelling Nonlinear Bivariate Dependence Using the Boubaker Polynomials Copula The Boubaker polynomials [13]
 ↑ 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 [14]
 ↑ El. Journal of theretical physics ( EJTP), M. Agida , A. S. Kumar, A Boubaker Polynomials Expansion Scheme Solution to Random Love’s Equation in the Case of a Rational Kernel [15]
 ↑ Modern Physics Letters B ([ISSN: 02179849, by WS: World Scientific Publishing Co Pte Ltd] ), S. Fridjine and M. Amlouk,A New ParameterAbacus for optimizing PVT Hybrid solar devices functional materials using Boubaker Polynomials Expansion Scheme [16]
 ↑ The definition of the Boubaker Poynomials, H. Bannour's Website [17]
 ↑ Recurrence relation for polynomial sequences via Riordan matrices, Pages 2425: BOUBAKER POLYNOMIALS associated Riordan matrix, A. Luzon and M. Moron [18]
 ↑ International Journal of the Franklin Institute (elsevier), A. S. Kumar , An analytical solution to applied mathematicsrelated Love's equation using the ‘’’Boubaker polynomials’’’ expansion scheme [19]
 ↑ Kiliç Bülent, Erdal Bas, Page 7, Citation 27: Boubaker polynomials , [20]
 ↑ C. R. Caldera and A. Milgram, , Notes on uniqueness of the Boubaker Polynomials Expansion Scheme (BPES) solution in the case of the Klein–Gordon equation ,Computers and Mathematics with Applications 62 (2011) 536–538, Elsevier [21]
 ↑ C. R. Caldera and A. Milgram, , Boubaker Polynomial Expansion Scheme BPES ternary materials optimization: A critical approach (Comment on a paper of MLBLUE),Material Letters (Elsevier) [22]
 ↑ B. Tirimula Rao, P. Srinivsu, C. Anantha Rao, K. Satya Vivek Vardhan, Jami Vidyadhari ,Page 8 : Boubaker polynomials ,[23]
External links[edit]
 Encyclopedia of Physics Research: citation title= Encyclopedia of Physics Research, Chapter 21: Cryogenics Vessels Thermal Profilng Using the Boubaker Polynomials, Editors: Nancy B. Devins and Jillian P. Ramos https://www.novapublishers.com/catalog/product_info.php?products_id=26337&osCsid=
 NASA: USAPhysics Abstract Service Database
 citationtitle=a New Parameter:. AN Abacus for Optimizing PvT Hybrid Solar Device Functional Materials Using the Boubaker Polynomials Expansion Scheme http://adsabs.harvard.edu/abs/2009MPLB...23.2179F and citationtitle= http://adsabs.harvard.edu/cgibin/nphdata_query?doi=10.1007/s002310090493x&db_key=PHY&link_type=ABSTRACT&high=499df58f2b32224
 citationtitle=De Khawarizmi à Eulerjournal=La Presse Magazinedate=January 9, 2008 http://www.lapresse.tn/index.php?opt=15&categ=4&news=63764 aussi tunisie7arts.com
 citationtitle=Le polynôme de Boubakerjournal=La Presse Magazinedate=April 22, 2007issue=1019page=6 http://www.lapresse.tn/pdf/magazine/20070423_weekend22042007.pdf fr
 citationtitle=A new polynomial sequence... The Boubaker Polynomialsjournal=Numerical Methods for Partial Differential Equations NMPDE http://www3.interscience.wiley.com/journal/120747691/abstract
 citationtitle=Solution to Heat Equation Using Boubaker Polynomialsjournal=J. of Thermophysics and Heat Transfer http://pdf.aiaa.org/jaPreview/JTHT/2009/PVJA40216.pdf
 citationtitle=Boubaker Polynomials Weak Solutions to a Robin Boundary Conditioned DynamicState Heat Transfer Problem journal=International Journal of Heat Transfer http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JHTRAO000131000011111305000001&idtype=cvips&gifs=yes
 WS World Scientific Publishing Co Pte Ltd
 citationtitle=AMLOUK–BOUBAKER EXPANSIVITY..USING BOUBAKER POLYNOMIALS journal=Functional Materials Letter http://www.worldscinet.com/fml/02/0201/S1793604709000533.html
 Academic Publications
 citationtitle=A new polynomial sequence ...The Boubaker Polynomialsjournal=International Journal of Applied Mathematics [24]
 Other papers NASA Astrophysics Data System
 ENEA Ente Nazionale per le Energie Alternative
 citationtitle=An attempt... using Boubaker Polynomialsjournal= International Journal of Heat and Technology http://termserv.casaccia.enea.it/eurotherm/indexHT.html
 citationtitle=Numerical Distribution of Temperature During Welding Using Boubaker Polynomials journal= Numerical Heat Transfer, Part A, Applications http://www.informaworld.com/smpp/content~db=all~content=a908590869?words=boubaker

 citationtitle=Establishment of an Ordinary Generating Function and a ChristoffelDarboux Type FirstOrder Differential Equation for the Heat Equation Related BoubakerTurki Polynomialsjournal= Journal of Differential Equations and C.P. http://www.neva.ru/journal/j/pdf/boubaker2.pdf
 citationtitle=Some new properties of the appliedphysics related Boubaker polynomials http://www.neva.ru/journal/j/pdf/zhao.pdf

 citation 3, Page 97 C.P.=http://www.ustarch.sav.sk/ustarch/reports/USTARCHSAV_Annual_Report_2010_up100211.pdf
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 MATH Database 1931 2011, © European Mathematical Society, FIZ Karlsruhe & SpringerVerlag


 Meixnertype results for Riordan arrays and associated integer sequences, Chap. 6 Boubaker Polynomials
 An analytical solution to applied mathematicsrelated 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
