Dept. of Mathematics
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(2015-12-02)Configuration Space on trees comes naturally from problems in engineering and has its own importance in mathematics. This paper reviewed the existing research results on the topological properties of classic configuration ...
(2015-12-04)In this thesis, we study supersaturation and enumeration problems in extremal combinatorics. In Chapter 2, with Balogh, we disprove a conjecture of Erdos and Tuza concerning the number of different ways one can create a ...
(2015-12-10)We study the bound states of the 1+1 dimensional Dirac equation with a scalar potential, which can also be interpreted as a position dependent "mass'', analytically as well as numerically. We derive a Prüfer-like representation ...
(2015-07-16)We consider here an extension and generalization of the stochastic neuronal network model developed by DeVille et al.; their model corresponded to an all-to-all network of discretized integrate-and-fire excitatory neurons ...
Ramanujan's identities, Voronoi summation formula, and zeros of partial sums of zeta and L-functions (2015-08-03)The focus of the first part of the thesis commences with an examination of two pages in Ramanujan's lost notebook, pages 336 and 335. A casual, or even more prolonged, examination of the strange formulas on these pages ...