Browsing by Subject "Continued fractions"
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Item Continued fractions(2011-08) Hannsz, Baron Kurt; Armendáriz, Efraim P.; Daniels, MarkThis report examines the theory of continued fractions and how their use enhances the secondary mathematics curriculum. The use of continued fractions to calculate best approximants of real numbers is justified geometrically, and famous irrational numbers are described as continued fractions. Periodic continued fractions and other applications of continued fractions are also discussed.Item Continued fractions and their application in the computation of definite Riemann integrals(Texas Tech University, 1973-08) Compton, Stanley MaxNot availableItem Floquet theory and continued fractions for harmonically driven systems(2003) Martinez Mantilla, Dario Fernando; Reichl, L. E.We derive an exact solution using continued fractions for a quantum particle scattering from an oscillating delta-function potential. We study its transmission properties such as: Transmission zeros, transmission poles and threshold anomalies. Using the same technique and a translation matrix method, we study the problem of an infinite chain of oscillating deltas. We calculate its band structure and eigenstates and show explicitly the contribution to these eigenstates from the quasi-bound state of a single oscillating delta. We study the dynamics of the quasi-energy bands of the system as a function of the strength of the oscillation and show band quasi-periodicity and band collapse. We also define the Floquet-Green’s function for a time-periodic Hamiltonian and by a generalization of the method used for the two previous potentials we are able to derive an expression for the Floquet-Green’s function of any harmonically driven Hamiltonian. As an example of the application of this method we study a tight-binding Hamiltonian with harmonic time dependence.Item The QD algoritm and its Application to the Transformation of Power Series Into Continued Fraction(Texas Tech University, 1971-08) Narayanaswami, SaraswathiNot Available.