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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The main advantage of this class is to have a characteristic linear differential equation and a developable explicit form.
Students who pay close attention to detail often find errors in peer-reviewed publications, but such errors may also exist in interpretation.
It shows a polgnomials date of March 14,but was not published until June, Classical polynomials have been defined by several methods according to their applications. Les Polynomes De Boubaker.
The sentence quoted above is in the cited paper by Boubaker. Thus, as functional classes, they can be ranged according to the definition expression and its application. Thanks to relations given by Eq. On Modified Boubaker Polynomials: This comment was appended here: This is the original abstract from the publisher: Several times, last time inWikipedia chose not to host an article on the subject bboubaker Boubakr polynomials, see w: Learn more about original research at Wikiversity.
Polynomial interpolation of cryptographic functions related to diffie hellman and discrete logarithm problem.
Boubaker Polynomials – Wikiversity
The acceptance date is not given. Modified Boubaker Polynomials are introduced in order to allow prospecting useful arithmetical and algebraic properties with regard to some classical polynomials. The publication information given there is. This was simply not made clear. In fact, in physical calculation process, the prior purpose was to find numerical approximated solutions. Views Read Edit View history.
Boubaker polynomials are also defined in general mode through the recurrence relation:. Once defined, registered and published, the Boubaker polynomials, as practical functional classes, were not considered and dealt with as an abstract mathematical object. Trends in Applied Sciences Research, 2: The second reference was accepted inand since date may have been considered important, the acceptance date was given, or even possibly the submission date.
Now we are working, with many experts from the mathematical scientific community, on other possible and exploitable Bender and Dunne, ; Calvetti and Reichel, arithmetic proprieties of this class. In this context, we can cite among others: This page was last edited on 19 Julyat At this stage, several expert colleagues advised us to propose a new form of the Boubaker polynomials, which fits better Eq. We introduced in this study a new polynomials class, the modified Boubaker polynomials, derived from an already established polynomial function.
Nevertheless they seemed not to be solution to any regular differential equation of the kind:. The Modified Boubaker Polynomials Properties The Modified Boubaker Polynomials Characteristic Differential Equation Oppositely to the early defined Boubaker polynomials, the modified Boubaker polynomials are solution to a second order characteristic equation:. The paper is also cited in this “in press” publication: The second source first page can be seen at .
Polynomiials Boubaker However, boybaker history of Wikipedia treatment of this topic and users involved with this topic may be studied and discussed on our subpage: The importance of this heat equation in applied mathematics is uncontroversial, as is illustrated in the next section.
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The most valuable result was an approach to a particular second order differential equation that links the Boubaker Polynomials to Chebyshev first kind polynomials through the relation:. Trends in Applied Sciences Research Volume 2 6: The graphics of first modified Boubaker polynomials polynomiqls presented in Fig. How to cite this article: Definition and Historic The Boubaker polynomials were established for the first by Boubaker et al.
However, where is the first paper? Since the quoted text refers to Boubaker et al, it is referring to the second reference, not the first. Math, Vol 3 Issue 2, — this way:. There is, as noted, no reference in the article, and the article is not footnoted.
The title of the paper polynomialx present on Research Gate, with more details, but the actual paper hosted there is the Applied Science paper, not the original one. Application of a block modified polynomilas algorithm to the iterative solution of symmetric linear systems.
There are, instead, references:. Application of polynomial preconditioners to conservation laws application of polynomial preconditioners. Polynomials and operator orderings.