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A New Graded Algebra Structure on Differential Polynomials: Level Grading and its Application to the Classification of Scalar Evolution Equations in 1+1 Dimension
New Graded Algebra Structure Differential Polynomials Level Grading Classification of Scalar Evolution Equations 1+1 Dimension
2012/4/26
We define a new grading, that we call the "level grading", on the algebra of polynomials generated by the derivatives $u_{k+i}=\partial^{k+i}u/\partial x^{k+i}$ over the ring $K^{(k)}$ of $C^{\infty}$...
Generating functions for the Bernstein polynomials: A unified approach to deriving identities for the Bernstein basis functions
Bernstein polynomials generating function Szasz-Mirakjan basis functions
2011/2/28
The main aim of this paper is to provide a unified approach to deriving identities for the Bernstein polynomials using a novel generating function. We derive various functional equations and different...