3. Electronic Theses and Dissertations (ETDs) - All submissions
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Item Darboux transformations on Sturm-Liouville eigenvalue problems with eigenparameter dependant transmission conditions(2017) Phalafala, Rakgwahla, JessicaSturm-Liouville eigenvalue problems arise prominently in mathematical physics. An innumerous amount of complexities have been encountered in solving these problems and a myriad of techniques have been explored over the century. In this work, we investigate one such technique, namely the Darboux-Crum trans formation. This transformation transforms an existing problem into one that is readily solvable or displays properties that are better understood. In particular, we focus our attention on the e↵ect the Darboux-Crum transformation has on the eigenparameter dependence of the transmission condition of our Sturm-Liouville eigenvalue problem.Item Hints of multi-matrix eigenvalue dynamics(2017) Gossman, David MichaelAfter studying matrix model quantum mechanics for one and two matrices and the eigenvalue dynamics of the one matrix model, evidence is found that there is a sector of the two matrix model that can be reduced to eigenvalue dynamics. This sector is defined by the SU(2) sector of N = 4 super Yang-Mills theory. Evidence is found by doing explicit computations of correlation functions using an interesting generalization of the usual Van der Monde determinant. The observables we study are the BPS operators of the SU(2) sector and include traces of products of both matrices, which are genuine multi matrix observables. These operators are associated to supergravity solutions of string theory.Item Eigenvalues of toeplitz determinants(1990) Coppin, GrahamThe Toeplitz form is a most useful and important teo! in many areas of applied. mathematics today including signal processing, time-series analysis and prediction theory. It is even used in quantum mechanics in Ising model correlation functions. (Abbreviation abstract)Item Inverse eigenvalue problem(2016-08-16) Boamah, Edward KwasiThis work is concerned with the Inverse Eigenvalue Problem for ordinary differential equations of the Sturm-Liouville type in the general form --dd ( 7' ()xdll(t\,:rI)) + {(q) x - t\p:(r )} u (A, Xl, = 0, .1' c.r (I :::: .7' S; b. The central problem considered ill this research is the approximate reC011- struction of the unknown coefficient function q(:l') in the Sturm-Liouville equation JOIl Irom a given finite spectral data set ~i(q), for i = 1 : n . A solution is sought using a finite element discretization method. The method works br solving the non-Iinear system arising out of the difference between the eigenvalues A,(q) of the Sturm-Liouville differential equation and the given spectral data ~i(q). Numerical results me presented to illustrate the effectiveness of the discretization method ill question.