# Category Archives: Graduate news

# The zeros of entire functions

Graduate student Rintaro “Yoshi” Yoshida will defend the degree of Ph.D. on Thursday May 2, 2:00pm, in Keller 301.

We invite the reader to consider the entire function

$$\varphi_{_{1/5}}(x) = \sum_{k=0}^\infty \frac{x^k}{(k!)^{(6/5)}}.$$

Do you think this function has any non-real zeros? Does it belong to the Laguerre-Pólya class? See the draft dissertation for answers.

# Nondeterministic finite state complexity

Graduate student Kayleigh Hyde will present her Master’s project on Monday April 22, 10:30am, in Shidler College of Business Room E201. Draft paper

Let $M$ be a nondeterministic finite automaton, having $q$ states and no $\epsilon$-transitions. If there is exactly one path through $M$ of length $n$ leading to an accept state, and $x$ is the string read along that path, then we say that $A_N(x)\le q$ (the NFS complexity of $x$ is at most $q$).