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Full-Text Articles in Algebraic Geometry
Invariants Of 3-Braid And 4-Braid Links, Mark Essa Sukaiti
Invariants Of 3-Braid And 4-Braid Links, Mark Essa Sukaiti
Theses
In this study, we established a connection between the Chebyshev polynomial of the first kind and the Jones polynomial of generalized weaving knots of type W(3,n,m).
Through our analysis, we demonstrated that the coefficients of the Jones polynomial of weaving knots are essentially the Whitney numbers of Lucas lattices which allowed us to find an explicit formula for the Alexander polynomial of weaving knots of typeW(3,n).
In addition to confirming Fox’s trapezoidal conjecture, we also discussed the zeroes of the Alexander Polynomial of weaving knots of type W(3,n) as they relate to Hoste’s conjecture. In addition, …
Numerical Solution For Solving Two-Points Boundary Value Problems Using Orthogonal Boubaker Polynomials, Imad Noah Ahmed
Numerical Solution For Solving Two-Points Boundary Value Problems Using Orthogonal Boubaker Polynomials, Imad Noah Ahmed
Emirates Journal for Engineering Research
In this paper, a new technique for solving boundary value problems (BVPs) is introduced. An orthogonal function for Boubaker polynomial was utilizedand by the aid of Galerkin method the BVP was transformed to a system of linear algebraic equations with unknown coefficients, which can be easily solved to find the approximate result. Some numerical examples were added with illustrations, comparing their results with the exact to show the efficiency and the applicability of the method.