Applications of graph theory to matrix theory

Applications of subordination theory to starlike functions

Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ ...

Some Applications of Graph Theory to Numbers Theory

Let al <. .. < ak s n be a sequence of integers no one of which divides any other. It 1s not difficult to see that max k-[Et'-) [1]. Assume now that no a i divides the product of two others, then I proved that [2] (r(x) denotes the number of primes c x2/3 (1) n (x) +-l Z < max k (t .9 =) not exceeding x) x 2/3 < e(x) + c 2 (tog =) 2 The proof of both the upper and the lower bound used combinato...

Applications of Large Cardinals to Graph Theory

Applications of graph theory to landscape genetics

We investigated the relationships among landscape quality, gene flow, and population genetic structure of fishers (Martes pennanti) in ON, Canada. We used graph theory as an analytical framework considering each landscape as a network node. The 34 nodes were connected by 93 edges. Network structure was characterized by a higher level of clustering than expected by chance, a short mean path leng...

Applications of random matrix theory to analytic number theory

This research proposal concerns several projects at the interface of analytic number theory and random matrix theory. As such the proposal involves ideas from number theory, combinatorics, and analysis. The proposal is divided into two sections, related by the perhaps surprising use they make of combinatorial representation theory, but also by the following theme: both sections will study a spe...