The paper deals with three-term recurrence relations for Boubaker and related polynomials, as well as some properties including zero. The Boubaker Polynomials Expansion Scheme for. Solving Applied-physics Nonlinear high-order Differential Equations. 1. Ugur Yücel and. 2. Karem Boubaker. Received August 14, Abstract—Some new properties of the Boubaker polynomials expansion scheme are presented in this paper. It is shown in particular.
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Enhancement of pyrolysis spray disposal performance using thermal time response to precursor uniform deposition. This is a direct quote from: Nevertheless they seemed not to be solution to any regular differential equation of the kind:. Classical polynomials have been defined by several methods according to their applications. Les Polynomes De Boubaker. At this stage, several expert colleagues advised us to propose a new form of the Boubaker polynomials, which fits better Eq.
The acceptance date is not given. Polynomials and operator orderings. Math, Vol 3 Issue 2, — this way:. Boubaker polynomials are the components of a polynomial sequence  :.
Thanks to relations given by Eq. Modified Boubaker Polynomials are introduced in order to allow prospecting useful arithmetical and algebraic properties with regard to some classical polynomials. Abstract In this study an attempt presented to establish a characteristic linear differential equation and an explicit form to the modified Boubaker polynomials The original Boubaker polynomials were established earlier as an effective tool for solving heat bi-varied equation in a particular case of one-dimensional heat transfer model.
However, where is the first paper?
Boubaker Polynomials – Wikiversity
Learn more about original research at Wikiversity. The Modified Boubaker Polynomials Properties The Modified Boubaker Polynomials Characteristic Differential Equation Oppositely to the early defined Boubaker polynomials, the modified Polynmials polynomials are solution to a second order characteristic equation:.
Views Read Edit View history. Once defined, registered and published, the Boubaker polynomials, as practical functional classes, were not considered and dealt with as an abstract mathematical object.
This is what is shown as to the original:. The sentence quoted above is in the cited paper by Boubaker. Polynomiale to cite this article: Another definition of Boubaker polynomials is:.
Blubaker we are working, with many experts from the mathematical scientific community, on other possible and exploitable Bender and Dunne, ; Bounaker and Reichel, arithmetic proprieties of this class. This was simply not made clear. The main polynomialx of this class is to have a characteristic linear differential equation and a developable explicit form. The second source first page can be seen at . Thus, as functional classes, they can be ranged according to the definition expression and its application.
This page was last edited on 19 Julyat There is, as noted, no reference in the article, and the article is not footnoted.
Karem Boubaker After several tests and trials, we set the new proposed polynomials, which are the modified Boubaker polynomials defined mainly by Eq. This comment was appended here: Boubaker polynomials have generated many integer sequences in the w: The paper is also cited in this “in press” publication: It shows a received date of March 14,but was not published until June, The boubaker polynomials a new function class for solving bi varied second order differential equations.
Definition and Historic The Boubaker polynomials were established for the first by Boubaker et al. The title of the paper is poljnomials on Research Gate, with more details, but the actual paper hosted there is the Applied Booubaker paper, not the original one.
Students who pay close attention to detail often find errors in peer-reviewed publications, but such errors may also exist in interpretation.
There are, instead, references:. Since the quoted text refers to Boubaker et al, it is referring to the second reference, not the first. This resource is about the polynomials and applications. On Modified Boubaker Polynomials: In fact, in physical calculation process, the prior purpose was to find numerical approximated solutions.
Retrieved from ” https: Subpage for the collection of sources on Boubaker polynomials: We present here to the worldwide scientific community, the modified Boubaker polynomials that are closer to mathematical analysis as long as they can be easily subjected to arithmetical and integral analysis.
The importance of this heat equation in applied mathematics is uncontroversial, as is illustrated in the next section.
In this context, we can cite among others: The early works on polynomials can be attributed to Al-Khawarizmi with his attempt to solve six canonical equations, followed by Omar Al-Khayyam who tried to solves cubics geometrically by intersecting conics Kiltz and Winterhof, The Modified Boubaker Polynomials Definition The Boubaker polynomials were tested and submitted to several studies from to Polynomial interpolation of cryptographic functions related to diffie hellman and discrete logarithm problem.
Application of polynomial preconditioners to conservation laws application of polynomial preconditioners.