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Dissertations / Theses on the topic 'Colouring'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 July 2025

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1

Chowdhury, Ameerah. "Colouring Subspaces." Thesis, University of Waterloo, 2005. http://hdl.handle.net/10012/1026.

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This thesis was originally motivated by considering vector space analogues of problems in extremal set theory, but our main results concern colouring a graph that is intimately related to these vector space analogues. The vertices of the <em>q</em>-Kneser graph are the <em>k</em>-dimensional subspaces of a vector space of dimension <em>v</em> over F<sub><em>q</em></sub>, and two <em>k</em>-subspaces are adjacent if they have trivial intersection. The new results in this thesis involve colouring the <em>q</em>-Kneser graph when <em>k</em>=2. There are two cases. When <em>k</em>=2 and <e

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2

Chu, Lei. "Colouring Cayley Graphs." Thesis, University of Waterloo, 2005. http://hdl.handle.net/10012/1125.

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We will discuss three ways to bound the chromatic number on a Cayley graph. 1. If the connection set contains information about a smaller graph, then these two graphs are related. Using this information, we will show that Cayley graphs cannot have chromatic number three. 2. We will prove a general statement that all vertex-transitive maximal triangle-free graphs on <i>n</i> vertices with valency greater than <i>n</i>/3 are 3-colourable. Since Cayley graphs are vertex-transitive, the bound of general graphs also applies to Cayley graphs. 3. Since Cayley graphs for a

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3

Quinn, Samuel. "Colouring naphthalene diimides." Thesis, University of Nottingham, 2018. http://eprints.nottingham.ac.uk/50038/.

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Naphthalene diimides have been explored in a wide variety of ways; They are a promising candidate for organic electronics, boasting the ability to form n-type semiconductor materials, the stability of their anions further aiding in this regard. Their electron poor aromatic core can be used in host guest chemistry to generate interlocked species. The ability to tune their electronic properties and how this could be manipulated to create photovoltaic devices is primarily focus of this thesis. A series of naphthalene diimides substituted at the core with morpholine moieties have been synthesized

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4

Nielsen, Steven Ole. "Colouring a Lorentz gas." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/MQ34034.pdf.

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5

Rackham, Tom. "Problems in graph colouring." Thesis, University of Oxford, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.526104.

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6

Williams, Jini. "Aspects of graph colouring." Thesis, Open University, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.410449.

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7

Kennedy, William. "Fractional edge and total colouring." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=106323.

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Many problems which seek to schedule, sequence, or time-table a set of events subject to given constraints can be modelled as graph colouring problems. In this thesis, we study the edge and total colouring problems which, like all NP problems, can be formulated as integer programs and subjected to a two-pronged attack: we first solve the fractional relaxation and then use this solution to solve or obtain an approximation of the solution of the integer program. We focus on the complexity of solving the fractional relaxations of the integer programs for the edge and total colouring problems. For

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8

Meagher, Conor John. "Fractionally total colouring most graphs." Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=18201.

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A total colouring is the assignment of a colour to each vertex and edge of a graph such that no adjacent vertices or incident edges receive the same colour and no edge receives the same colour as one of its endpoints. If we formulate the problem of finding the total chromatic number as an integer program, we can consider the fractional relaxation known as fractional total colouring. In this thesis we present an algorithm for computing the fractional total chromatic number of a graph, which runs in polynomial time on average. We also present an algorithm that asymptotically almost surely comput

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9

Gerke, Stefanie. "Weighted colouring and channel assignment." Thesis, University of Oxford, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325977.

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10

Watts, Ivor Llewellyn. "Overlap and fractional graph colouring." Thesis, Open University, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.505353.

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Although a considerable body of material exists concerning the colouring of graphs, there is much less on overlap colourings. In this thesis, we investigate the colouring of certain families of graphs.

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11

Mcgrae, Allen. "Colouring empires in random trees." Thesis, University of Liverpool, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.533988.

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12

Waters, Robert James. "Graph colouring and frequency assignment." Thesis, University of Nottingham, 2005. http://eprints.nottingham.ac.uk/10135/.

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In this thesis we study some graph colouring problems which arise from mathematical models of frequency assignment in radiocommunications networks, in particular from models formulated by Hale and by Tesman in the 1980s. The main body of the thesis is divided into four chapters. Chapter 2 is the shortest, and is largely self-contained; it contains some early work on the frequency assignment problem, in which each edge of a graph is assigned a positive integer weight, and an assignment of integer colours to the vertices is sought in which the colours of adjacent vertices differ by at least the

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13

Song, Jian. "Graph colouring with input restrictions." Thesis, Durham University, 2013. http://etheses.dur.ac.uk/6998/.

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In this thesis, we research the computational complexity of the graph colouring problem and its variants including precolouring extension and list colouring for graph classes that can be characterised by forbidding one or more induced subgraphs. We investigate the structural properties of such graph classes and prove a number of new properties. We then consider to what extent these properties can be used for efficiently solving the three types of colouring problems on these graph classes. In some cases we obtain polynomial-time algorithms, whereas other cases turn out to be NP-complete. We det

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14

Farrugia, Alastair. "Uniqueness and Complexity in Generalised Colouring." Thesis, University of Waterloo, 2003. http://hdl.handle.net/10012/1018.

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The study and recognition of graph families (or graph properties) is an essential part of combinatorics. Graph colouring is another fundamental concept of graph theory that can be looked at, in large part, as the recognition of a family of graphs that are colourable according to certain rules. In this thesis, we study additive induced-hereditary families, and some generalisations, from a colouring perspective. Our main results are: · Additive induced-hereditary families are uniquely factorisable into irreducible families. · If <i>P</i> and <i>Q</i> are additive induced-here

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15

Batchelor, Oliver William. "Ray Traversal for Incremental Voxel Colouring." Thesis, University of Canterbury. Computer Science and Software Engineering, 2006. http://hdl.handle.net/10092/1143.

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Image based scene reconstruction from multiple views is an interesting challenge, with many ambiguities and sources of noise. One approach to scene reconstruction is Voxel Colouring, Seitz and Dyer [26], which uses colour information in images and handles the problem of occlusion. Culbertson and Malzbender [11], introduced Generalised Voxel Colouring (GVC) which uses projection and rasterization to establish global scene visibility. Our work has involved investigating the use of ray traversal as an efficient alternative. We have developed two main approaches along this line, Ray Images

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16

Rocha, Leonardo Sampaio. "Algorithmic aspects of graph colouring heuristics." Nice, 2012. https://tel.archives-ouvertes.fr/tel-00759408.

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Une coloration propre d’un graphe est une fonction qui attribue une couleur à chaque sommet du graphe avec la restriction que deux sommets voisins ont des couleurs distinctes. Les colorations permettent de modéliser des problèmes d’ordonnancement, d’allocation de fréquences ou de registres. Le problème de trouver une coloration propre d’un graphe qui minimise le nombre de couleurs est un problème NP-difficile très connu. Dans cette thèse nous étudions le nombre de Grundy et le nombre b-chromatique des graphes, deux paramètres qui permettent d’évaluer quelques heuristiques pour le problème d’e

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17

Ali, Seema. "Colouring generalized Kneser graphs and homotopy theory." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0014/MQ34938.pdf.

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18

Lienart, Emmanuelle Anne Sophie. "Edge-colouring and I-factors in graphs." Thesis, Goldsmiths College (University of London), 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325549.

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19

MuÌˆller, Tobias. "Random geometric graphs : colouring and related topics." Thesis, University of Oxford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.437019.

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20

Gao, Rong. "Some colouring problems for Pseudo-Random Graphs." Thesis, University of Essex, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.494355.

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21

Forbes, Anthony Duncan. "Configurations and colouring problems in block designs." Thesis, Open University, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.435910.

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22

Lord, Gwynn Arthur. "A biochemical investigation of food colouring agents." Thesis, Manchester Metropolitan University, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.279013.

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23

Coker, Thomas David. "Graph colouring and bootstrap percolation with recovery." Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610806.

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24

Ferguson, David G. "Topics in graph colouring and graph structures." Thesis, London School of Economics and Political Science (University of London), 2013. http://etheses.lse.ac.uk/735/.

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This thesis investigates problems in a number of different areas of graph theory. These problems are related in the sense that they mostly concern the colouring or structure of the underlying graph. The first problem we consider is in Ramsey Theory, a branch of graph theory stemming from the eponymous theorem which, in its simplest form, states that any sufficiently large graph will contain a clique or anti-clique of a specified size. The problem of finding the minimum size of underlying graph which will guarantee such a clique or anti-clique is an interesting problem in its own right, which h

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25

Hardy, Bradley. "Heuristic methods for colouring dynamic random graphs." Thesis, Cardiff University, 2018. http://orca.cf.ac.uk/109385/.

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Many real-world operational research problems can be reformulated into static graph colouring problems. However, such problems might be better represented as dynamic graphs if their size and/or constraints change over time. In this thesis, we explore heuristics approaches for colouring dynamic random graphs. We consider two di�erent types of dynamic graph: edge dynamic and vertex dynamic. We also consider two di�erent change scenarios for each of these dynamic graph types: without future change information (i. e. random change) and with probabilistic future change information. By considering a

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26

Feghali, Carl. "Topics in graph colouring and extremal graph theory." Thesis, Durham University, 2016. http://etheses.dur.ac.uk/11790/.

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In this thesis we consider three problems related to colourings of graphs and one problem in extremal graph theory. Let $G$ be a connected graph with $n$ vertices and maximum degree $\Delta(G)$. Let $R_k(G)$ denote the graph with vertex set all proper $k$-colourings of $G$ and two $k$-colourings are joined by an edge if they differ on the colour of exactly one vertex. Our first main result states that $R_{\Delta(G)+1}(G)$ has a unique non-trivial component with diameter $O(n^2)$. This result can be viewed as a reconfigurations analogue of Brooks' Theorem and completes the study of reconfigurat

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27

Achlioptas, Demetrios. "Threshold phenomena in random graph colouring and satisfiability." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape7/PQDD_0002/NQ41090.pdf.

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28

Turvill, Michael W. "The synthesis of natural and synthetic colouring materials." Thesis, University of Nottingham, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.280103.

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29

Purcell, Christopher. "Cliques, colouring and satisfiability : from structure to algorithms." Thesis, University of Warwick, 2013. http://wrap.warwick.ac.uk/60496/.

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We examine the implications of various structural restrictions on the computational complexity of three central problems of theoretical computer science (colourability, independent set and satisfiability), and their relatives. All problems we study are generally NP-hard and they remain NP-hard under various restrictions. Finding the greatest possible restrictions under which a problem is computationally difficult is important for a number of reasons. Firstly, this can make it easier to establish the NP-hardness of new problems by allowing easier transformations. Secondly, this can help clarify

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30

Rombach, Michaela Puck. "Colouring, centrality and core-periphery structure in graphs." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:7326ecc6-a447-474f-a03b-6ec244831ad4.

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Krivelevich and Patkós conjectured in 2009 that χ(G(n, p)) ∼ χ=(G(n, p)) ∼ χ∗=(G(n, p)) for C/n < p < 1 − ε, where ε > 0. We prove this conjecture for n−1+ε1 < p < 1 − ε2 where ε1, ε2 > 0. We investigate several measures that have been proposed to indicate centrality of nodes in networks, and find examples of networks where they fail to distinguish any of the vertices nodes from one another. We develop a new method to investigate core-periphery structure, which entails identifying densely-connected core nodes and sparsely-connected periphery nodes. Finally, we present an experiment and an anal

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31

Kang, Ross J. "Improper colourings of graphs." Thesis, University of Oxford, 2008. http://ora.ox.ac.uk/objects/uuid:a93d8303-0eeb-4d01-9b77-364113b81a63.

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We consider a generalisation of proper vertex colouring of graphs, referred to as improper colouring, in which each vertex can only be adjacent to a bounded number t of vertices with the same colour, and we study this type of graph colouring problem in several different settings. The thesis is divided into six chapters. In Chapter 1, we outline previous work in the area of improper colouring. In Chapters 2 and 3, we consider improper colouring of unit disk graphs -- a topic motivated by applications in telecommunications -- and take two approaches, first an algorithmic one and then an average-

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32

Gellert, Laura Kristin [Verfasser]. "On problems related to graph colouring / Laura Kristin Gellert." Ulm : Universität Ulm, 2017. http://d-nb.info/1147484511/34.

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33

Sant, Paul. "Algorithmics of edge-colouring pairs of 3-regular trees." Thesis, King's College London (University of London), 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.406705.

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34

Titiloye, Olawale. "Optimization by quantum annealing for the graph colouring problem." Thesis, Manchester Metropolitan University, 2013. http://e-space.mmu.ac.uk/324247/.

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Quantum annealing is the quantum equivalent of the well known classical simulated annealing algorithm for combinatorial optimization problems. Despite the appeal of the approach, quantum annealing algorithms competitive with the state of the art for specific problems hardly exist in the literature. Graph colouring is a difficult problem of practical significance that can be formulated as combinatorial optimization. By introducing a symmetry-breaking problem representation, and finding fast incremental techniques to calculate energy changes, a competitive graph colouring algorithm based on quan

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35

Egger, Salome. "The rays are colouring : the encounter of a phenomenon." Thesis, Nottingham Trent University, 2017. http://irep.ntu.ac.uk/id/eprint/34666/.

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This doctoral research, fusing the fields of Art, Science and Technology, explores the physical colour phenomenon of metamerism, by offering a theoretical account and aesthetic experience of the impact of light on dyed and knitted textiles through a series of artistic scenarios. In the field of colour and colour management the focus of research has generally been on how to avoid 'problematic' metameric colours due to their shifting visual coherence in varying light sources. However, this 'practice as research' project investigates metameric colours through textile installations and performance

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36

Salvador, Villà Marta. "[r,s,t]-colouring of paths, cycles and stars." [S.l. : s.n.], 2005. https://fridolin.tu-freiberg.de/archiv/html/MathematikSalvador%5FVillXMarta925466.html.

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37

Skjernaa, Bjarke. "Exact algorithms for variants of satisfiability and colouring problems /." BRICS, 2004. http://www.brics.dk/DS/04/5/BRICS-DS-04-5.pdf.

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38

Naqvi, Kazim Raza. "Role of transition metal ions in oxidative hair colouring." Thesis, University of York, 2014. http://etheses.whiterose.ac.uk/6955/.

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The objective of this Ph.D. project was to study the role of transition metal ions in oxidative hair colouring. Model systems corresponding to real-life hair colouring conditions were designed to examine copper(II) and iron(III) catalysed decomposition of alkaline hydrogen peroxide and hydroxyl radical formation. In a chelant-free system, copper(II) ions were more active in decomposing alkaline hydrogen peroxide compared to iron(III) ions. For copper(II) ions, the initial rate of decomposition of hydrogen peroxide and hydroxyl radical formation increased with an increase in initial concentrati

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39

Lignos, Ioannis. "Reconfigurations of combinatorial problems : graph colouring and Hamiltonian cycle." Thesis, Durham University, 2017. http://etheses.dur.ac.uk/12098/.

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We explore algorithmic aspects of two known combinatorial problems, Graph Colouring and Hamiltonian Cycle, by examining properties of their solution space. One can model the set of solutions of a combinatorial problem $P$ by the solution graph $R(P)$, where vertices are solutions of $P$ and there is an edge between two vertices, when the two corresponding solutions satisfy an adjacency reconfiguration rule. For example, we can define the reconfiguration rule for graph colouring to be that two solutions are adjacent when they differ in colour in exactly one vertex. The exploration of the proper

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40

Drew, Neil. "Colouring-in - a distraction technique? : a study looking at the effects of colouring-in for adults in reducing negative affect and state rumination." Thesis, University of Exeter, 2018. http://hdl.handle.net/10871/34176.

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Background Adult colouring books have become increasingly popular in recent years, with suggestions that they can reduce stress and increase calmness, but there is currently a limited evidence base in this area. This study explored whether colouring-in is more effective than a neutral distraction activity and rumination in improving affect and state rumination after experiencing a laboratory stressor that involved solving difficult anagrams. Method The study was a mixed (3 x 3) experimental design, with condition as the between-subjects factor (distraction, colouring-in, rumination) and time a

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41

Howard, David John. "Colouring the nation : race and ethnicity in the Dominican Republic." Thesis, University of Oxford, 1997. http://ora.ox.ac.uk/objects/uuid:e7cc675f-cd66-4827-a52f-9cd1765f3777.

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This thesis analyses the importance of race for the construction of nation and ethnicity in the Dominican Republic, a situation in which racial ancestry and spatial proximity to Haiti are paramount. Firstly, racial legacies are of primary importance among a Dominican population where cultural, linguistic and religious differences are limited. Racial differences are manipulated through the unequal standing and significance given to European, African and indigenous ancestries. European and indigenous heritages in the Dominican Republic have been celebrated at the expense of an African past. Seco

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42

Smith, Marilyn. "The colouring, sealing and abrasion resistance of anodic oxide coatings." Thesis, London Metropolitan University, 1990. http://repository.londonmet.ac.uk/2981/.

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The service performance of anodised aluminium in architecture is dependent upon the control of the anodising, colouring and sealing processes. The quality of the anodic oxide film is determined by assessment tests. The use of a nitric acid ‘predip’ on soft films was shown to dissolve a soft outerlayer. A new admittance test was devised in which the ‘drift’, Y, was measured using 33%, nitric acid. This test threw light on the sealing quality of films exposed to the environment and those sealed in nickel salt solutions. Well-sealed, hard films gave a Y value of 0.1 to 0.2. A sealing mechanism fo

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43

Bingham, Stephen John. "The total synthesis of carminic acid." Thesis, Brunel University, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.260260.

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44

Kirkham, Ruth S. "Wing pattern determination and wing colour development in Heliconius melpomene (lepidoptera)." Thesis, University of Nottingham, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.236498.

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45

Sulong, Ghazali bin. "Algorithms for timetable construction." Thesis, Cardiff University, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.253664.

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46

Thompson, Russell Martin. "Nitrosylmetalloporphyrin complexes as models for cured meat pigments." Thesis, University of Surrey, 1988. http://epubs.surrey.ac.uk/848117/.

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A range of nitrosylmetalloporphyrin complexes, M(porph)NO [M = Fe, Co; porph = TPP, OEP, T[PIV]PP], some labelled with [15]NO, has been synthesised and investigated as structural and spectroscopic models of the cured meat pigment, nitrosylmyoglobin. The nitrosylmetalloporphyrins were found to be unstable in solution (and some in the solid state) with respect to loss or further reaction of the nitrosyl ligand. The diamagnetic cobalt (III) porphyrin nitrosyIs and a range of other square pyramidal complexes of cobalt(III) with an apical nitrosyl ligand have been further investigated by [15]N and

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47

Sinner, Alain Thomas Yvon. "'Protective colouring' : the political commitment in the poetry of Seamus Heaney." Thesis, University of Hull, 1988. http://hydra.hull.ac.uk/resources/hull:3154.

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48

Singh, Navreen K. "Does colouring promote mindfulness and enhance wellbeing? : a randomised controlled trial." Thesis, University of Surrey, 2018. http://epubs.surrey.ac.uk/849293/.

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Objectives: Colouring books for adults have become increasingly popular. Some of these books are marketed on the basis that they improve mindfulness and promote wellbeing. Using a randomised design, this study aimed to empirically explore whether the provision of guidance on how to colour mindfully is necessary to increase mindfulness, and to reduce worry, perceived stress and work-related rumination. Moreover, the study aimed to assess whether changes in mindfulness predicted changes in worry, perceived stress and work-related rumination. The extent to which trait perfectionism might impact o

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49

Howlett, Rory John. "The genetics and evolution of rest-site preference in the lepidoptera." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.277869.

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50

Zhang, Peng. "A study on generalized solution concepts in constraint satisfaction and graph colouring." Thesis, University of British Columbia, 2014. http://hdl.handle.net/2429/50022.

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The concept of super solutions plays a crucial role in using the constraint satisfaction framework to model many AI problems under uncertain, dynamic, or interactive environments. The availability of large-scale, dynamic, uncertain, and networked data sources in a variety of application domains provides a challenge and opportunity for the constraint programming community, and we expect that super solutions will continue to attract a great deal of interest. In the first part of this thesis, we study the probabilistic behaviour of super solutions of random instances of Boolean Satisability (SAT)

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