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Full-Text Articles in Physical Sciences and Mathematics
The Operator (Sgn X) D²/Dx² Is Similar To A Selfadjoint Operator In L² (R), Branko Ćurgus, Branko Najman
The Operator (Sgn X) D²/Dx² Is Similar To A Selfadjoint Operator In L² (R), Branko Ćurgus, Branko Najman
Mathematics Faculty Publications
Krein space operator-theoretic methods are used to prove that the operator (sgn x) d²/dx² is similar to a selfadjoint operator in the Hilbert space L²(R).
Lazutkin Coordinates And Invariant Curves For Outer Billiards, Edoh Y. Amiran
Lazutkin Coordinates And Invariant Curves For Outer Billiards, Edoh Y. Amiran
Mathematics Faculty Publications
The outer billiard ball map (OBM) is defined from and to the exterior of a domain, Ω, in the plane as taking a point, q, to another point, q 1, when the line segment with endpoints q and q 1 is tangent to the boundary, ∂Ω (with a chosen orientation), and the point of tangency with the boundary divides the segment in half. Let C be an invariant circle for the OBM on Ω, with ∂Ω smooth with positive curvature. After computing the loss of derivatives between ∂Ω and C, it is shown via KAM theory that …
Historical Development Of The Newton-Raphson Method, Tjalling Ypma
Historical Development Of The Newton-Raphson Method, Tjalling Ypma
Mathematics Faculty Publications
This expository paper traces the development of the Newton-Raphson method for solving nonlinear algebraic equations through the extant notes, letters, and publications of Isaac Newton, Joseph Raphson, and Thomas Simpson. It is shown how Newton's formulation differed from the iterative process of Raphson, and that Simpson was the first to give a general formulation, in terms of fluxional calculus, applicable to nonpolynomial equations. Simpson's extension of the method to systems of equations is exhibited.