Browse Items (9 total)

Generic arguments lead to the idea that quantum gravity has a minimal length scale. A possible observational signal of such a minimal length scale is that photons should exhibit dispersion. In 2009, the observation of a short gamma ray burst seemed…

We extend the well-known characterizations of convergence in the spaces lp (1 ≤ p < ∞) of p-summable sequences and c0 of vanishing sequences to a general characterization of convergence in a Banach space with a Schauder basis and obtain as instant…

We study the zero distribution of the sum of the first n polynomials satisfying a three-term recurrence whose coefficients are linear polynomials. We also extend this sum to a linear combination, whose coefficients are powers of az + b for a, b ∈ R,…

Typically, undergraduates see real analysis as one of the most difficult courses that a mathematics major is required to take. The main reason for this perception is twofold: Students must comprehend new abstract concepts and learn to deal with these…

This paper begins with a survey of some applications of Khovanov homology to low-dimensional topology, with an eye toward extending these results to sl(n) homologies. We extend Levine-Zemke’s ribbon concordance obstruction from Khovanov homology to…

The L-move for classical braids extends naturally to trivalent braids. We follow the L-move approach to the Markov theorem to prove a one-move Markov-type theorem for trivalent braids. We also reformulate this L-move Markov theorem and prove a more…

In quantum gravity it is generally thought that a modified commutator of the form [(x) over cap, (p) over cap] = ih(1 + beta p(2)) is sufficient to give rise to a minimum length scale. We test this assumption and find that different pairs of modified…

Current approaches to quantum gravity suggest there should be a modification of the standard quantum mechanical commutator, [x^,p^]=iℏ. Typical modifications are phenomenological and designed to result in a minimal length scale. As a motivating…