After being introduced to graph theory and realizing how it can be utilized to solve real-world problems, the author decided to create modules of study on graph theory appropriate for middle school students. In this thesis, four modules were developed in the area of graph theory: an Introduction to Terms and Definitions, Graph Families, Graph Operations, and Graph Coloring. It is written as a guide for middle school teachers to prepare teaching units on graph theory.

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Cartographers utilize primary and secondary colors in producing color maps. It is relatively easy to print the primary colors of magenta, cyan, and yellow on photo paper. It is considerably more difficult to print the secondary colors of red, blue, green, orange, purple, seagreen, and leafgreen consistently.This thesis has solved the problem associated with producing photographic color for cartographic maps. A new system of developing color maps has been developed. This system has produced: (1) pure blacks, (2) suitable secondary colors, (3) pastel colors, and (4) mid-value and dark colors.

Dating back to the 1930's, Ramsey theory still intrigues many who study combinatorics. Roughly put, it makes the profound assertion that complete disorder is impossible. One view of this problem is in edge-colorings of complete graphs. For forbidden graphs H1,...,Hk and a graph G, we write G "arrows" (H1,...,Hk) if every k-edge-coloring of G contains a monochromatic copy of Hi in color i for some i=1,2,...,k. If c is a (red, blue)-edge-coloring of G, we say c is a bad coloring if G contains no red K3or blue K1,t under c. A graph G is (H1,...,Hk)-Ramsey-minimal if G arrows (H1,...,Hk) but no proper subgraph of G has this property. Given a family F of graphs, we say that a graph G is F-saturated if no member of F is a subgraph of G, but for any edge xy not in E(G), G + xy contains a member of F as a subgraph. Letting Rmin(K3, K1,t) be the family of (K3,K1,t)-Ramsey minimal graphs, we study the saturation number, denoted sat(n,Rmin(K3,K1,t)), which is the minimum number of edges among all Rmin(K3,K1,t)-saturated graphs on n vertices. We believe the methods and constructions developed in this thesis will be useful in studying the saturation numbers of (K4,K1,t)-saturated graphs.

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京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第21770号 / 工博第4587号 / 新制||工||1715(附属図書館) / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 中村 裕一, 教授 小山田 耕二, 教授 喜多 一 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

SAMMANFATTNING  Syfte  Syftet med studien var att undersöka huruvida färginfiltrering med effektfärg påverkar böjhållfastheten i flerskiktad zirkonia.  Material och metod Zirkoniamaterialet KATANA™ Zirconia YML, Kuraray Noritake användes i studien. Totalt framställdes 54 stycken provkroppar varav sex stycken utgjorde en pilotstudie för polering. Resterande 48 delades in i sex grupper (n = 8). Tre av grupperna frästes ut från Emalj och Body 1 (E-B1) och de resterande tre grupperna frästes ut från Body 2 och Body 3 (B2-B3). Två grupper, från de olika skikten, infiltrerades med Esthetic Colorant A plus (A), två grupper infiltrerades med Esthetic Colorant Opaque (O) samt två grupper utgjorde kontrollgrupper utan infiltrering (K). Provkropparna infiltrerades och sintrades enligt fabrikantens anvisningar. Därefter polerades de enligt ett poleringsschema och slutligen genomfördes ett biaxialt böjhållfasthetstest. Resultaten från samtliga grupper analyserades med One-way ANOVA, Tukey’s test, med en signifikansnivå på α = 0,05 med hjälp av statistikprogrammet SPSS.  Resultat Resultatet påvisade ingen signifikant skillnad i böjhållfastheten inom grupperna för de två skikten (E-B1A, E-B1O och E-B1K) samt (B2-B3A, B2-B3O och B2-B3K). Grupperna med skikten som inkluderade B2-B3 uppvisade signifikant högre böjhållfasthet oavsett infiltrering/kontroll än grupperna E-B1A, E-B1O och E-B1K.   Slutsats Böjhållfastheten i flerskiktad zirkonia påverkas inte av infiltrering med effektfärg. / ABSTRACT Purpose The purpose of this in vitro study was to investigate whether color infiltration with effect colors affect the biaxial flexural strength of multilayer zirconia.   Material and method The zirconia material KATANA™ Zirconia YML, Kuraray Noritake was used in the study. A total of 54 specimens were produced, of which six were part of a pilot study for polishing. The remaining 48 were divided into six groups (n=8). Three of the groups were milled of Enamel and Body 1 (E-B1) and the remaining three groups were milled of Body 2 and Body 3 (B2-B3). Two groups, from the different layers, were colored with Esthetic Colorant A plus (A), two groups were colored with Esthetic Colorant Opaque (O), while two groups served as control groups (K). The specimens were colored and sintered according to the manufacturer's instructions, polished according to a polishing schedule, and finally a biaxial flexural strength test was performed. The results were analyzed using One-way ANOVA, Tukey's test, with a significance level of α = 0.05 using the statistical software SPSS.   Results The results showed no significant difference in flexural strength within the groups for the two layers (E-B1A, E-B1O, and E-B1K) and (B2-B3A, B2-B3O, and B2-B3K). The groups with layers that included B2-B3 showed significantly higher flexural strength regardless of coloring/control than the groups E-B1A, E-B1O, and E-B1K.  Conclusion The flexural strength of multilayered zirconia is not affected by color infiltration with effect colors.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第25089号 / 理博第4996号 / 新制||理||1714(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 COLLINSBenoit Vincent Pierre, 教授 泉 正己, 准教授 山下 真由子 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DFAM