Vertex-distinguishing edge-colorings (vdec colorings) are a restriction of proper edge-colorings. These special colorings require that the sets of edge colors incident to every vertex be distinct. This is a relatively new field of study. We present a survey of known results concerning vdec colorings. We also define a new matrix which may be used to study vdec colorings, and examine its properties. We find several bounds on the eigenvalues of this matrix, as well as results concerning its determinant, and other properties. We finish by examining related topics and open problems.

A major question in Knot Theory concerns the process of trying to determine when two knots are different. A knot invariant is a quantity (number, polynomial, group, etc.) that does not change by continuous deformation of the knot. One of the simplest invariant of knots is colorability. In this thesis, we study Fox colorings of knots and knots that are colored by linear Alexander quandles. In recent years, there has been an interest in reducing Fox colorings to a minimum number of colors. We prove that any Fox coloring of a 13-colorable knot has a diagram that uses exactly five colors. The ideas behind the reduction of colors in a Fox coloring is extended to knots colored by linear Alexander quandles. Thus, we prove that any knot colored by either the linear Alexander quandle Z5[t]/(t − 2) or Z5[t]/(t − 3) has a diagram using only four colors.

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Leung Bo-Shan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 148-159). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgements --- p.v / List of Abbreviations --- p.vi / List of Tables --- p.viii / List of Figures --- p.ix / Chapter 1 --- Introduction / Chapter 1.1 --- Food colorants --- p.1 / Chapter 1.2 --- Caramel --- p.3 / Chapter 1.2.1 --- Classes of caramel --- p.3 / Chapter 1.2.2 --- Toxicological studies of caramel --- p.5 / Chapter 1.3 --- Castanea mollissima --- p.9 / Chapter 1.4 --- Antioxidants --- p.10 / Chapter 1.4.1 --- Background --- p.10 / Chapter 1.4.2 --- Methods used to evaluate the antioxidative activity --- p.12 / Chapter 1.4.2.1 --- DPPH* scavenging method --- p.13 / Chapter 1.4.2.2 --- High performance liquid chromatography (HPLC) --- p.13 / Chapter 1.5 --- Microtox® test --- p.19 / Chapter 1.6 --- Mutatox® test --- p.19 / Chapter 1.7 --- Methods used to evaluate the functions of major organs --- p.20 / Chapter 1.7.1 --- Liver --- p.20 / Chapter 1.7.2 --- Kidneys --- p.23 / Chapter 1.8 --- Toxicology --- p.25 / Chapter 1.8.1 --- Acute toxicity test --- p.25 / Chapter 1.8.2 --- Chronic toxicity test --- p.26 / Chapter 1.9 --- Objective --- p.27 / Chapter 2 --- Materials and Methods --- p.28 / Chapter 2.1 --- Plant materials --- p.28 / Chapter 2.2 --- Sample preparation --- p.28 / Chapter 2.3 --- Pigment characterization --- p.30 / Chapter 2.3.1 --- Stability test --- p.30 / Chapter 2.3.2 --- HPLC separation of CP --- p.31 / Chapter 2.3.3 --- Determination of antioxidative activity with the DPPH* scavenging method --- p.31 / Chapter 2.4 --- Microtox® test --- p.33 / Chapter 2.5 --- Mutatox® test --- p.34 / Chapter 2.6 --- Acute toxicity test --- p.35 / Chapter 2.6.1 --- Animals --- p.35 / Chapter 2.6.2 --- Housing and maintenance --- p.35 / Chapter 2.6.3 --- Experimental design --- p.37 / Chapter 2.6.4 --- Chemicals --- p.39 / Chapter 2.6.5 --- Clinical pathology test --- p.41 / Chapter 2.6.5.1 --- Haematology --- p.41 / Chapter 2.6.5.2 --- Blood chemistry --- p.45 / Chapter 2.6.5.3 --- Urinalysis --- p.55 / Chapter 2.6.6 --- Histological study --- p.57 / Chapter 2.6.7 --- Statistical analysis --- p.57 / Chapter 2.7 --- Chronic toxicity test --- p.59 / Chapter 2.7.1 --- Animals --- p.59 / Chapter 2.7.2 --- Housing and maintenance --- p.59 / Chapter 2.7.3 --- Experimental design --- p.59 / Chapter 2.7.4 --- Chemicals --- p.60 / Chapter 2.7.5 --- Clinical pathology test --- p.61 / Chapter 2.7.5.1 --- Haematology --- p.61 / Chapter 2.7.5.2 --- Blood chemistry --- p.62 / Chapter 2.7.5.3 --- Urinalysis --- p.62 / Chapter 2.7.6 --- Histological study --- p.62 / Chapter 2.7.7 --- Statistical analysis --- p.62 / Chapter 3 --- Results --- p.63 / Chapter 3.1 --- Pigment characterization --- p.63 / Chapter 3.1.1 --- Stability test --- p.63 / Chapter 3.1.2 --- HPLC separation of CP --- p.63 / Chapter 3.1.3 --- Antioxidative activities of CP preparations --- p.63 / Chapter 3.2 --- Microtox® test --- p.65 / Chapter 3.3 --- Mutatox® test --- p.65 / Chapter 3.4 --- Acute toxicity test --- p.66 / Chapter 3.4.1 --- Growth rate --- p.66 / Chapter 3.4.2 --- Food and fluid consumption --- p.66 / Chapter 3.4.3 --- Organ-weight --- p.66 / Chapter 3.4.4 --- Clinical pathology tests --- p.68 / Chapter 3.4.4.1 --- Haematology --- p.68 / Chapter 3.4.4.2 --- Blood chemistry --- p.70 / Chapter 3.4.4.3 --- Urinalysis --- p.76 / Chapter 3.4.5 --- Histological study --- p.76 / Chapter 3.5 --- Chronic toxicity test --- p.77 / Chapter 3.5.1 --- Growth rate --- p.77 / Chapter 3.5.2 --- Food and fluid consumption --- p.77 / Chapter 3.5.3 --- Organ-weight --- p.77 / Chapter 3.5.4 --- Clinical pathology tests --- p.78 / Chapter 3.5.4.1 --- Haematology --- p.78 / Chapter 3.5.4.2 --- Blood chemistry --- p.80 / Chapter 3.5.4.3 --- Urinalysis --- p.82 / Chapter 3.5.5 --- Histological study --- p.82 / Chapter 4 --- Discussion --- p.137 / Chapter 4.1 --- Pigment characterization --- p.137 / Chapter 4.2 --- Toxicological studies of CP --- p.140 / Chapter 5 --- Conclusion --- p.147 / References --- p.148

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A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. December 2014. / Let G be a finite group and let r ∈ N. A coloring of G is any mapping : G −→ {1, 2, 3, ..., r}. Colorings of G, and are equivalent if there exists an element g in G such that (xg−1) = (x) for all x in G. A coloring of a finite group G is called symmetric with respect to an element g in G if (gx−1g) = (x) for all x ∈ G. We derive formulae for computing the number of symmetric colorings and the number of equivalence classes of symmetric colorings for some classes of finite groups

OBJECTIVES: To investigate the effect of different alumina fabrication techniques and sintering temperatures on the biaxial flexural strength. Also, to assess the resulting color of multiple metal salt solutions at different concentrations in monolithic alumina and its effect on the optical properties of the restoration. MATERIAL & METHOD: Forty disk-shape alumina specimens were divided into 4 groups (n=10) based on the fabrication process (slip cast or die press) and sintering temperature (1530°C or 1600°C). Biaxial flexural strength was calculated using universal testing machine at a crosshead speed rate of 0.5 mm/min until failure occurred. For the coloring part of the study, nine elements (Ba, Ce, Cr, Fe, Mn, Nd, Pr, Sm, Zn) were used to form metal-salt coloring solutions at a concentration of 0.1%, 1% and 5% wt. The solutions were then used to infuse 162 pre-sintered porous alumina disks that are either slip-casted (A1000) or die-pressed (CT3000). Color coordinates were recorded in CIE L*a*b* system using spectrophotometer. Color differences relative to the control (ΔE), translucency parameter (TP), contrast ratio (CR) and total transmission were calculated and analyzed using two-way analysis of variance (ANOVA) with Tukey post hoc test at α = 0.05. RESULTS: Slip cast group sintered at 1530°C had the highest flexural strength (479.14 MPa), but there was no significant difference between the four groups neither by fabrication process (p = 0.127) nor by sintering temperature (p = 0.276). Die press specimens colored with Ba at 0.1% and 1% showed significantly higher TP (2.65 and 2.49) and lowest CR (96.15 and 96.30) among the groups. There was a statistically significant effect on TP and CR when changing alumina powder on specimens colored by Ba, Ce, and Zn (p < 0.05). Changing the concentration of the coloring solution caused a significant effect on the optical properties of specimens colored by Ba, Nd, Cr, Mn. ΔE was significantly changed when changing alumina powder and coloring concentration for all elements except Ce, Pr, and Sm. CONCLUSION: Changing fabrication method and sintering temperature did not affect the biaxial flexural strength. However, the fabrication method and metal-salt colorant concentration affected the optical properties of the specimens. / https://hdl.handle.net/2144/35681

Yeung Kit Ying. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 98-106). / Abstracts in English and Chinese. / Acknowledgements --- p.i / Abstract --- p.ii / List of Abbreviations --- p.iv / List of Tables --- p.v / List of Figures --- p.vi / Chapter 1 --- Introduction / Chapter 1.1 --- Botany --- p.1 / Chapter 1.2 --- Food additives and food preservation --- p.2 / Chapter 1.2.1 --- Lipid peroxidation --- p.2 / Chapter 1.2.2 --- Role of food antioxidant --- p.4 / Chapter 1.2.3 --- Microbial spoilage --- p.5 / Chapter 1.2.4 --- Additives in future --- p.6 / Chapter 1.3 --- Antioxidant and health benefits effects --- p.7 / Chapter 1.4 --- Measurement of antioxidants --- p.7 / Chapter 1.4.1 --- Trolox equivalent antioxidant capacity (TEAC) assay --- p.8 / Chapter 1.4.2 --- DPPH radical scavenging assay --- p.9 / Chapter 1.4.3 --- β-carotene bleaching assay --- p.9 / Chapter 1.4.4 --- Assay for erythrocyte hemolysis mediated by peroxyl free radicals --- p.10 / Chapter 1.4.5 --- Measurement of lipid peroxidation in foods --- p.10 / Chapter 1.5 --- Antiproloiferative studies --- p.12 / Chapter 1.5.1 --- MTT assay --- p.12 / Chapter 1.5.2 --- Cell Proliferation ELISA-BrdU (chemiluminescence) assay --- p.13 / Chapter 1.5.3 --- Cytotoxicity detection assay (LDH) --- p.13 / Chapter 1.6 --- Characterization of phenolic compounds --- p.14 / Chapter 1.6.1 --- Sephadex column chromatography --- p.14 / Chapter 1.6.2 --- Folin and Ciocalteu's assay --- p.15 / Chapter 1.7 --- Research objectives --- p.15 / Chapter 2 --- Materials and Methods / Chapter 2.1 --- Standards and reagents --- p.22 / Chapter 2.2 --- Plant materials --- p.23 / Chapter 2.3 --- Pigment preparation --- p.23 / Chapter 2.4 --- Determination of antioxidant activity --- p.25 / Chapter 2.4.1 --- Trolox equivalent antioxidant capacity (TEAC) assay --- p.25 / Chapter 2.4.2 --- DPPH. radical scavenging assay --- p.26 / Chapter 2.4.3 --- β-carotene bleaching assay --- p.26 / Chapter 2.4.4 --- Assay for erythrocyte hemolysis mediated by peroxyl free radicals --- p.27 / Chapter 2.4.4.1 --- Determination of IC50 --- p.28 / Chapter 2.5 --- Evaluation of CP as antioxidant in various food models --- p.28 / Chapter 2.5.1 --- Preparation of food samples --- p.28 / Chapter 2.5.2 --- Butter cookies --- p.29 / Chapter 2.5.3 --- Salad dressing --- p.29 / Chapter 2.5.4 --- Fried potato chips --- p.29 / Chapter 2.5.5 --- PeroXOquant´ёØ quantitative peroxide assay --- p.29 / Chapter 2.5.6 --- Statistical analysis --- p.30 / Chapter 2.6 --- Determination of antimicrobial activity --- p.31 / Chapter 2.6.1 --- Determination of antimicrobial activity --- p.31 / Chapter 2.6.1.1 --- Bacterial stock --- p.31 / Chapter 2.6.1.2 --- Preparation of nutrient agar plate --- p.31 / Chapter 2.6.1.3 --- Minimal inhibiting concentration (MIC) --- p.31 / Chapter 2.6.2 --- Determination of antifungal activity --- p.32 / Chapter 2.6.2.1 --- Fungi stock --- p.32 / Chapter 2.6.2.2 --- Preparation of potato dextrose agar plates --- p.32 / Chapter 2.6.2.3 --- Growth inhibition effect --- p.32 / Chapter 2.6.3 --- Statistical analysis --- p.33 / Chapter 2.7 --- In vitro effect on human cell lines --- p.34 / Chapter 2.7.1 --- Cell lines --- p.34 / Chapter 2.7.2 --- Maintenance of cell lines --- p.34 / Chapter 2.7.3 --- MTT assay --- p.35 / Chapter 2.7.4 --- Cell Proliferation ELISA-BrdU (chemiluminescence) assay --- p.36 / Chapter 2.7.5 --- Determination of IC50 --- p.37 / Chapter 2.7.6 --- Cytotoxicity detection assay --- p.37 / Chapter 2.7.6.1 --- Optimal cell concentration --- p.37 / Chapter 2.7.6.2 --- LDH detection assay --- p.38 / Chapter 2.7.7 --- Statistical analysis --- p.39 / Chapter 2.8 --- Fractionation and characterization --- p.40 / Chapter 2.8.1 --- Sephadex column chromatography --- p.40 / Chapter 2.8.2 --- Fourier transform infrared (FT-IR) spectra --- p.40 / Chapter 2.8.3 --- Folin and Ciocalteu's assay --- p.40 / Chapter 2.8.4 --- Statistical analysis --- p.41 / Chapter 3 --- Results / Chapter 3.1 --- Determination of antioxidant activity --- p.43 / Chapter 3.1.1 --- Trolox equivalent antioxidant capacity (TEAC) assay --- p.43 / Chapter 3.1.2 --- DPPH.radical scavenging assay --- p.43 / Chapter 3.1.3 --- β-carotene bleaching assay --- p.44 / Chapter 3.1.4 --- Assay for erythrocyte hemolysis mediated by peroxyl free radicals --- p.44 / Chapter 3.2 --- Potential application as food antioxidant --- p.45 / Chapter 3.2.1 --- Peroxide standard curve --- p.45 / Chapter 3.2.2 --- Inhibition of lipid peroxidation in different food items --- p.45 / Chapter 3.3 --- Potential application as food preservative --- p.46 / Chapter 3.3.1 --- Antibacterial activity --- p.46 / Chapter 3.3.2 --- Antifungal activity --- p.46 / Chapter 3.4 --- In vitro effect on human cell lines --- p.47 / Chapter 3.4.1 --- Effect on the growth of human cancer cells --- p.47 / Chapter 3.4.2 --- Antiproliferative effect on selected human cancer cells --- p.48 / Chapter 3.4.3 --- Cytotoxicity effect on selected human cancer cells and normal fibroblast --- p.48 / Chapter 3.4.3.1 --- Optimal cell density for cytotoxicity determined assay --- p.48 / Chapter 3.4.3.2 --- Cytotoxic effect --- p.48 / Chapter 3.5 --- Fractionation and characterization --- p.49 / Chapter 3.5.1 --- Percentage of yield --- p.49 / Chapter 3.5.2 --- Fourier transform infrared (FT-IR) spectra --- p.49 / Chapter 3.5.3 --- Determination of total phenolic content --- p.49 / Chapter 3.5.4 --- Determination of antioxidant activity --- p.50 / Chapter 3.5.5 --- Relationship between total phenolics and antioxidant activity --- p.50 / Chapter 3.5.6 --- Antiproliferative effect on cancer cell --- p.50 / Chapter 3.5.7 --- Cytotoxic effect --- p.51 / Chapter 3.5.7.1 --- HepG2 human cancer cell line --- p.51 / Chapter 3.5.7.2 --- Hs68 human normal fibroblast --- p.51 / Chapter 4 --- Discussion / Chapter 4.1 --- Application of CP as a natural food additive with multi-functions --- p.87 / Chapter 4.1.1 --- CP as a natural food antioxidant --- p.88 / Chapter 4.1.2 --- CP as a natural food preservative --- p.90 / Chapter 4.2 --- Potential health-beneficial --- p.91 / Chapter 4.2.1 --- CP as dietary antioxidant --- p.91 / Chapter 4.2.2 --- Antiproliferative activity of CP --- p.92 / Chapter 4.3 --- Further characterization of CP --- p.94 / Chapter 4.4 --- Future perspectives --- p.96 / Chapter 5 --- Conclusion --- p.97 / References --- p.98

Neste trabalho abordamos o problema de coloraÃÃo de vÃrtices via programaÃÃo inteira. Uma versÃo expandida da formulaÃÃo por conjuntos independentes à utilizada para abrigar outras sub-estruturas do grafos alÃm dos vÃrtices. Cada uma dessas sub-estruturas define uma restriÃÃo que determina quantos conjuntos independentes sÃo necessarios para cobrir aquele subgrafo. Experimentos com um mÃtodo de geraÃÃo de cortes e colunas para o problema sÃo feitos para determinar um limite inferior para um conjunto de instÃncias classicas para esse problema a biblioteca DIMACS. / In this work the vertex coloring problem is approached via integer programming. A tighter version of the independent set formulation is used, where the vertex-related constraints are substituted by subgraph-related constraints. Each constraint establishes a lower bound on the number of independent sets intersecting a subgraph H. It is shown a sufficient condition for this inequality to define a facet of the associated polytope. Basically, H is required to be color critical, not included in another color critical subgraph, and to have a connected complement. Also, the column generation algorithm proposed by Mehotra and Trick (INFORMS Journal in Computing, 1996) is adapted to allow the addition of cutting planes and to provide lower bounds along the process, which may abbreviate its end. Some computational experiments are reported.