The University of North Carolina at Greensboro Regional Undergraduate Mathematics Conference Abstracts

It was a very chaotic day, says Kathryn Sikes. Indeed, mutants spread everywhere, according to Brian Stadler. Bacterial wars raged all over the place, adds Dan MacMartin. Everybody was stealing, reported Christian Sykes. There were no limits to it, witnessed by Samuel Grundman. Only the fittest survived and got out of the prison, noted by Joseph Krenicky. The group was set free by Steven Piantadosi. We almost got lost in cyclic paths, said Heather Allmond. At least, our weight was a perfect number, smiles Michael Shiver, because we were not oversized thanks to Martha Shott. Finally, a picture was taken by Gavin Taylor and you could win a date if you listened to David Dombrowski. Math can be a lot of fun

Invariant subspaces of X∗∗X^{**} under the action of biconjugates

summary:We study conditions on an infinite dimensional separable Banach space $X$ implying that $X$ is the only non-trivial invariant subspace of $X^{**}$ under the action of the algebra $\mathbb{A}(X)$ of biconjugates of bounded operators on $X$: $\mathbb{A}(X)=\lbrace T^{**}\: T \in \mathcal {B}(X)\rbrace$. Such a space is called simple. We characterize simple spaces among spaces which contain an isomorphic copy of $c_{0}$, and show in particular that any space which does not contain $\ell _1$ and has property (u) of Pelczynski is simple

Notes on Gabriel\u27s Horn

A smooth bounded solid of finite volume and infinite surface is constructed. It is a variant of the classical Gabriel’s horn that is often taught in Calculus classes

On Weak * Kadec-Klee Norms

Abstract. We present partial positive results supporting a conjecture that admitting an equivalent Lipschitz (or uniformly) weak * Kadec-Klee norm is a three space property

A Game-Theoretic Model of Monkeypox to Assess Vaccination Strategies

A Game-Theoretic Model of Monkeypox to Assess Vaccination Strategies Sri Vibhaav Bankaru, Depts. of Biomedical Engineering, Math, & Chemistry, Samuel Kossol, William Hou, & Parsa Mahmoudi, with Dr. Jan Rychtar, Dept. of Mathematics Monkeypox (MPX) is a zoonotic disease similar to smallpox. Its fatality rate is about 11% and it is endemic to the Central and West African countries. In this paper, we analyze a compartmental model of MPX dynamics. Our goal is to see whether MPX can be controlled and eradicated by voluntary vaccinations. We show that there are three equilibria - disease free, fully endemic and previously neglected semi-endemic (with disease existing only among humans). The existence of semi-endemic equilibrium has severe implications should the MPX virus mutate to increased viral fitness in humans. We find that MPX is controllable and can be eradicated in a semi-endemic equilibrium by vaccination. However, in a fully endemic equilibrium, MPX cannot be eradicated by vaccination alone.https://scholarscompass.vcu.edu/uresposters/1296/thumbnail.jp

Overexpression of the auxin binding PROTEIN1 modulates PIN-dependent auxin transport in tobacco cells

Background: Auxin binding protein 1 (ABP1) is a putative auxin receptor and its function is indispensable for plant growth and development. ABP1 has been shown to be involved in auxin-dependent regulation of cell division and expansion, in plasma-membrane-related processes such as changes in transmembrane potential, and in the regulation of clathrin-dependent endocytosis. However, the ABP1-regulated downstream pathway remains elusive. Methodology/Principal Findings: Using auxin transport assays and quantitative analysis of cellular morphology we show that ABP1 regulates auxin efflux from tobacco BY-2 cells. The overexpression of ABP1can counterbalance increased auxin efflux and auxin starvation phenotypes caused by the overexpression of PIN auxin efflux carrier. Relevant mechanism involves the ABP1-controlled vesicle trafficking processes, including positive regulation of endocytosis of PIN auxin efflux carriers, as indicated by fluorescence recovery after photobleaching (FRAP) and pharmacological manipulations. Conclusions/Significance: The findings indicate the involvement of ABP1 in control of rate of auxin transport across plasma membrane emphasizing the role of ABP1 in regulation of PIN activity at the plasma membrane, and highlighting the relevance of ABP1 for the formation of developmentally important, PIN-dependent auxin gradients