for K a compact subset of A and W an open subset of B [2]1. Now let X and Y be Hausdorff spaces, and let Z be an arbitrary topological space. Let XX Y be the topological product of X and Y. We shall be concerned with the compact-open topologized spaces Zxxr, Zx, and (ZX)Y. R. H. Fox [2] has related these spaces, taking Zx as compact-open topologized, but not considering topologies on the more c...

Backens recently proved that the ZX-calculus is complete for an important subset of quantum mechanics, namely stabilizer quantum mechanics, i.e. that for stabilizer quantum mechanics, any equation that can be shown to hold in the Dirac formalism can also be shown to hold within the ZX-calculus[2]. For her proof, she relied on operations on a special class of quantum states, namely graph states....

This paper presents a symmetric monoidal and compact closed bicategory that categorifies the zx-calculus developed by Coecke and Duncan. The 1-cells in this bicategory are certain graph morphisms that correspond to the string diagrams of the zx-calculus, while the 2-cells are rewrite rules.

Objective: The aim of this study was to compare the diagnostic efficacy of an electronic apex locator (EAL) and radiovisigraphy (RVG) in working length (WL) determination. Materials and Methods: This study was performed on Single-rooted maxillary/mandibular teeth requiring root canal treatment. After administration of local anesthesia, the teeth were isolated and the pulp cavities were accessed...

iii Acknowledgements v 1 Background 1 1.1 Process theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 A bit of category theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 A distinction between classical and quantum systems . . . . . . . . . . 4 1.4 Particularly important maps . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.5 Spiders . . . . . . ....

BACKGROUND This in vitro study compared the shaping ability of RaCe, FlexMaster, and ProFile rotary nickel-titanium instruments in severely curved root canals of extracted teeth. MATERIAL AND METHODS Sixty maxillary molars with curvatures ranging from 25° to 65° were embedded in a muffle system and portioned into five horizontal sections (thickness 1.2 mm), starting from the apex. Canals were...