Weyl Tensors, Strongly Regular Graphs, Multiplicative Characters, and a Quadratic Matrix Equation

Let $S$ be a real symmetric $n\times n$-matrix with zeros on the diagonal and let $\theta$ be a real number. We show that the set of quadratic equations $$\sum_{k}S_{i,k}S_{k,j}+S_{i,j}^2=\theta S_{i,j},\text { for }i<j,$$ has solutions $(S,\theta)$, with $S\neq0$, in all dimensions $n\geq 4$. % The equations originate from a question about the Riemannian curvature tensor. Our solutions relate the equations to strongly regular graphs, to group rings, and to multiplicative characters of finite fields

Confluence Graphs of Unitals

We show that the cliques of maximal size in the confluence graph of an arbitrary unital of order $q>2$ have size $q^2$, and that these cliques are the pencils of all blocks through a given point. This solves the Erd\H{o}s-Ko-Rado problem for all unitals. We also determine all maximal cliques of the confluence graph of the Hermitian unitals. As an application, we show that the confluence graph of an arbitrary unital unambiguously determines the unital. Along the way, we show that each linear space with $q^2$ points such that the sizes of both point rows and line pencils are bounded above by $q+1$ embeds in a projective plane of order $q$

Study of glucose transporters in C. elegans

The calorie restriction (CR) and insulin/IGF-I-like signalling (IIS) are two pathways regulating the lifespan of C. elegans. Recent studies showed that glucose restriction extends the lifespan of C. elegans while excessive glucose shortens the lifespan of the worms. The first step of the glucose metabolism is the transport of glucose across the plasma membrane by the glucose transporters. The work described in this thesis aims to identify glucose transporters in C. elegans and to provide a primary investigation of the in vitro and in vivo function of the identified glucose transporter. Nine putative transporters have been cloned and expressed. Out of the nice cloned putative transporters in the C. elegans genome, H17B01.1 (H17) only is identified as a fully functional glucose transporter using an oocyte expression system in which glucose transport activity is directly measured. The two transcripts of H17 are both capable of transporting glucose with high affinity, as well as transporting trehalose. Heterologous expression of H17 in mammalian CHO-T cells suggests that the protein is localised both on the plasma membrane and in the cytosol. In vitro studies of H17 show that the protein does not respond to insulin stimulation when expressed in mammalian CHO-T cell and rat primary adipocyte systems. In vivo functional studies using H17 RNAi indicate that the worm’s lifespan is not affected by the H17 knockdown. However, glucose metabolism of C. elegans (as measured by glucose oxidation to CO2 and incorporation into fat reserves) is influenced by the decreased expression of H17, especially in the daf-2 mutant strain, e1370. However, the increase of glucose metabolism caused by H17 knockdown observed in daf-2 mutant is inhibited in the age-1 and akt-1 mutant strains. The findings reported in this thesis suggest that the H17 glucose transporter may play an important role glucose metabolism in C. elegans and that this transport and metabolism is influenced by insulin receptor activity and serine kinase cascades.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Slanted symplectic quadrangles

By "slanting" symplectic quadrangles W(F) over fields F, we obtain very simple examples of non-classical generalized quadrangles. We determine the collineation groups of these slanted quadrangles and their groups of projectivities. No slanted quadrangle is a topological quadrangle