We generalize the notion of regular polyhedral subdivision of a point (or vector) configuration in a new direction. This is done after studying some related objects, like the finest regular coarsening and the regularity tree of a subdivision. Properties of these two objects are derived, which confer more structure to the class of non-regular subdivisions, relating them to its (in a sense) close...

We consider the following problem: Given a set S of graphs, each of n vertices, construct an nvertex planar graph G containing all the graphs of S as subgraphs. We distinguish the variant in which any two graphs of S are required to have disjoint edges in G (known as ’packing’) from the variant in which distinct graphs of S can share edges in G (called ’squeezing’). About the packing variant we...

Let $K$ be the function field of a curve $C$ over $\mathbb{F}$ either odd or zero characteristic. Following work by Serre and Mason on $\mathrm{SL}_2$, we study action arithmetic subgroups $\mathrm{SU}(3)$ its corresponding Bruhat-Tits tree associated to suitable completion $K$. More precisely, prove that quotient graph "looks like spider", in sense it is union set cuspidal rays (the "legs"), p...

The edge-distinguishing chromatic number (EDCN) of a graph $G$ is the minimum positive integer $k$ such that there exists vertex coloring $c:V(G)\to\{1,2,\dotsc,k\}$ whose induced edge labels $\{c(u),c(v)\}$ are distinct for all edges $uv$. Previous work has determined EDCN paths, cycles, and spider graphs with three legs. In this paper, we determine petal two petals loop, cycles one chord, fou...

Spider diagrams are a recently developed visual logic that make statements about relationships between sets, their members and their cardinalities. By contrast, the study of regular languages is one of the oldest active branches of computer science research. The work in this thesis examines the previously unstudied relationship between spider diagrams and regular languages. In this thesis, the ...

The use of a standardized beat sampling method for estimating spruce spider mite, Oligonychus ununguis (Jacobi) (Acari: Tetranychidae), densities on a widely used evergreen ornamental plant species, Juniperus chinensis variety 'Sargentii' A. Henry (Cupressaceae), was examined. There was a significant positive relationship between total spruce spider mite densities and spider mite densities from...

The aim of this thesis is to present an extension to the string graphs of Dixon, Duncan and Kissinger that allows the finite representation of certain infinite families of graphs and graph rewrite rules, and to demonstrate that a logic can be built on this to allow the formalisation of inductive proofs in the string diagrams of compact closed and traced symmetric monoidal categories. String dia...

Spiders are poorly studied in Iran, based on the latest studies the spider fauna of Iran includes 394 species in 126 genera belonging to 36 families. Considering the climatic and geographical variation of Iran, it can be assumed that Iran has a rich spider fauna compared to the adjacent countries. The present study seeks to take a new step in the ongoing active research of Iranian spider fauna....

Although spider bites can produce dermonecrotic wounds, the differential diagnosis of such lesions is extensive. Most of the conditions in the differential are far more common than spider bites. Thus, we suggest that you approach the complaint of a "spider bite" with a skeptical eye. Here we describe the clinical features of spider bites and summarize the treatment options. We also examine the ...

Although spider bites can produce dermonecrotic wounds, the differential diagnosis of such lesions is extensive. Most of the conditions in the differential are far more common than spider bites. Thus, we suggest that you approach the complaint of a "spider bite" with a skeptical eye. Here we describe the clinical features of spider bites and summarize the treatment options. We also examine the ...