This thesis examines the quantification of uncertainty in real-world engineering systems using the multilevel Monte Carlo method. It is often infeasible to use the traditional Monte Carlo method to investigate the impact of uncertainty because computationally it can be prohibitively expensive for complex systems. Therefore, the newer multilevel method is investigated and the cost of this method is analysed in the finite element framework. The Monte Carlo and multilevel Monte Carlo methods are compared for two prototypical examples: structural vibrations and buoyancy driven flows through porous media. In the first example, the impact of random mass density is quantified for structural vibration problems in several dimensions using the multilevel Monte Carlo method. Comparable eigenvalues and energy density approximations are found for the traditional Monte Carlo method and the multilevel Monte Carlo method, but for certain problems the expectation and variance of the quantities of interest can be computed over 100 times faster using the multilevel Monte Carlo method. It is also tractable to use the multilevel method for three dimensional structures, where the traditional Monte Carlo method is often prohibitively expensive. In the second example, the impact of uncertainty in buoyancy driven flows through porous media is quantified using the multilevel Monte Carlo method. Again, comparable results are obtained from the two methods for diffusion dominated flows and the multilevel method is orders of magnitude cheaper. The finite element models for this investigation are formulated carefully to ensure that spurious numerical artefacts are not added to the solution and are compared to an analytical model describing the long term sequestration of CO2 in the presence of a background flow. Additional cost reductions are achieved by solving the individual independent samples in parallel using the new podS library. This library schedules the Monte Carlo and multilevel Monte Carlo methods in parallel across different computer architectures for the two examples considered in this thesis. Nearly linear cost reductions are obtained as the number of processes is increased.

Wu, Nip Po. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also Chinese.

本論文工作主要包括三部分: (i) 含吡啶基-1-氮雜烯丙基配體的二价鍺氯化物的反應研究； (ii) 含吡啶基-1-氮雜烯丙基配體的一价鍺二聚體的合成及反應研究; (iii) 膦亞胺配體衍生的低价態第十四族金屬復合物及金屬亞乙烯的合成與反應研究。 / 第一章描述含吡啶基-1-氮雜烯丙基配位體的二价鍺氯化物66的反應。化合物66與Na[M(η⁵-C₅H₅)(CO)₃]2DME (M = Mo or W)反應，得到含鍺(II)-金屬單鍵的異核雙金屬鍺亞乙烯化合物76及77。化合物66與環戊二烯鈉反應生成了環戊二烯基取代的鍺烯。作為路易斯鹼，化合物66與大位阻硼烷的反應得到研究。化合物66與B(C₆F₅)₃反應，得到路易斯酸-鹼加合物79。此外，化合物66與三价氯化鎵及三价氯化銦進行的配體轉移反應也得到研究。另外，化合物66與水的反應產生[{HNC(Ph)CH(C₅H₄N-2)}GeCl] (82)。 / 第二章描述化合物66的還原化學。二价鍺氯化物66與過量鎂反應得到 [N(SiMe₃)C(Ph)C(SiMe₃) (C₅H₄N-2)Mg(μ-Cl)(THF)]₂ (110)和[C(Ph)C(SiMe₃)(C₅H₄N-2)]₂Ge₂ (111)的混合物。而其與過量金屬鋰反應則得到一价鍺二聚體[C(Ph)C(SiMe₃)(C₅H₄N-2)]₂Ge₂ (111)及[N(SiMe₃)C(Ph)C(SiMe₃) (C₅H₄N-2)]₂Ge₂ (112)。化合物66與等當量石墨鉀反應，主要得到一价鍺二聚體112。化合物112與偶氮苯反應得到鍺聯氨衍生物[PhNGe{N(SiMe₃) C(Ph)C(SiMe₃)(C₅H₄N-2)}]₂₋(113)。化合物112的路易斯鹼性得到研究。化合物112與一當量九羰基二鐵反應生成新型不對稱一价鍺二聚體[{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)(Fe(CO)₄)- Ge-Ge{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)}](114)，而其與兩當量九羰基二鐵反應則得到[{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)Fe(CO)₄)Ge]₂(115)。此外，二聚體112與硫磺進行反應，得到首個鍺二硫代羧酸酐的鍺類似物。 / 第三章介紹從膦亞胺配體衍生的二价態第十四族金屬復合物的合成，描述了由配體Ph₂P(2-CH₂Py)=NSiMe₃ (119)及H₂C(PPh₂=NSiMe₃)₂ (121)衍生的二价鍺及二价錫化合物的合成。此外，本章研究了半穏定配體Ph₂PCH₂(PPh₂=NSiMe₃) (131)的配位化學。化合物131在Bu[superscript n]Li及Bu[superscript n]₂Mg的作用下金屬化分解反應，分別生成膦亞胺鋰化合物[Li{CH(PPh₂)(PPh₂=NSiMe₃)}(THF)₂] (194)及鎂化合物[Mg{CH(PPh₂)(PPh₂=NSiMe₃)}₂] (193)。化合物194與相應的二价金屬氯化物反應得到1,3-二錫環丁烷196和1,3-二鉛環丁烷200。化合物194與二氯化鍺二噁烷配合物的反應得到新型三核雜環化合物195。此外，化合物196與九羰基二鐵反應，得到膦穏定的錫亞乙烯197。 / 第四章為第一至第三章的總結。 / This thesis is focused on three areas: (i) the reactivities of pyridyl-1-azaallyl germanium(II) chloride; (ii) the synthesis and reactivities of pyridyl-1-azaallyl germanium(I) dimer; (iii) the synthesis and reactivities of low-valent main group 14 metal complexes and metallavinylidenes derived from phosphoranoimines. / Chapter 1 describes the reactivities of pyridyl-1-azaallyl germanium(II) chloride [{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)}GeCl] (66). The reaction of 66 with Na[M(η⁵-C₅H₅)(CO)₃]2DME (M = Mo or W) affords heterobimetallic germylenes 76 and 77 which contain a germanium(II)-metal single bond. A Cp-substituted germylene was prepared from the reaction of 66 with sodium cyclopentadienylide. The Lewis base behavior of 66 toward bulky borane was investigated. Treatment of 66 with B(C₆F₅)₃ leads to the formation of a Lewis acid-base adduct 79. Furthermore, the ligand transfer reaction of 66 with GaCl₃ and InCl₃ were studied. In addition, the reaction of 66 with water affords [{HNC(Ph)CH(C₅H₄N-2)}GeCl] (82). / Chapter 2 describes the reduction chemistry of 66. Treatment of 66 with excess magnesium tunings affords a mixture of products [N(SiMe₃)C(Ph)C(SiMe₃)- (C₅H₄N-2)Mg(μ-Cl)(THF)]₂ (110) and [C(Ph)C(SiMe₃)(C₅H₄N-2)]₂Ge₂ (111). The reaction of 66 with an excess of lithium metals leads to a mixture of germanium(I) dimers [C(Ph)C(SiMe₃)(C₅H₄N-2)]₂Ge₂ (111) and [N(SiMe₃)C(Ph)C(SiMe₃)- (C₅H₄N-2)]₂Ge₂ (112). When compound 66 was treated with one equivalent of potassium graphite, compound 112 was obtained as the major product. The reaction of 112 with azobenzene affords the 1,2-digermylene hydrazinide [PhNGe{N(SiMe₃) C(Ph)C(SiMe₃)(C₅H₄N-2)}]₂ (113). The Lewis base behaviour of 112 was studied. Treatment of 112 with one equivalent of diironnonacarbonyl gives a new unsymmetric germanium(I) dimer [{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)(Fe(CO)₄)- Ge-Ge{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)}] (114), while the reaction of 112 with two equivalent of diironnonacarbonyl leads to the formation of [{N(SiMe₃)C- (Ph)C(SiMe₃)(C₅H₄N-2)Fe(CO)₄)Ge]₂ (115). In addition, the reaction of 112 with sulfur affords the first germanium analogue of a dithiocarboxylic acid anhydride. / Chapter 3 deals with the synthesis of group 14 metal(II) complexes supported by iminophosphoranyl ligands. The synthesis of germanium(II) and tin(II) compounds derived from Ph₂P(2-CH₂Py)=NSiMe₃ (119) and H₂C(PPh₂=NSiMe₃)₂ (121) are described. Furthermore, the coordination chemistry of the hemilabile ligand Ph₂PCH₂(PPh₂=NSiMe₃) (131) was investigated. Iminophosphoranyl phosphine 131 undergoes metalation with Bu[superscript n]Li and Bu[superscript n]₂Mg to give the lithium complex [Li{CH(PPh₂)(PPh₂=NSiMe₃)}(THF)₂] (194) and the magnesium complex [Mg{CH- (PPh₂)(PPh₂=NSiMe₃)}₂] (193), respectively. 1,3-distannylcyclobutane 196 and 1,3-diplumbacyclobutane 200 were prepared from the reaction of 194 with the corresponding metal(II) chlorides. The reaction of 194 with GeCl₂(dioxane) leads to a tri-nuclear heterocyclic cage compound 195. In addition, the trapping reaction of 196 with diironnonacarbonyl affords the phoshpine-stabilized stannavinylidene 197. / Chapter 4 describes the conclusion of the first three chapters. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Chiu, Wang Kin. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in also in Chinese. / Tables of Contents --- p.vi / Acknowledgments --- p.i / Abstract --- p.ii / 摘要 --- p.iv / List of Compounds Synthesized --- p.xiv / Abbreviations --- p.xvi / Chapter Chapter 1 --- Reactivity of Pyridyl-1-azaallyl Germanium(II) Chloride / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.1.1 --- Reactivity Study of Heteroleptic Organogermanium(II) Chlorides --- p.1 / Chapter 1.1.2 --- Synthesis and Structure of Pyridyl-1-azaallyl Germanium(II) Chloride --- p.13 / Chapter 1.1.3 --- Objectives --- p.15 / Chapter 1.2 --- Results and Discussion --- p.18 / Chapter 1.2.1.1 --- Synthesis of Metallo-germylenes from Pyridy1-1-azaallyl Germanium (II) chloride --- p.19 / Chapter 1.2.1.2 --- Spectroscopic Properties of [{N(SiMe₃)C(Ph)C(SiMe₃)- (C₅H₄N-2)}Ge-M(η⁵-C₅H₅)(CO)₃] (M = Mo (76), W (77) --- p.19 / Chapter 1.2.1.3 --- Molecular Structures of [{N(SiMe₃)C(Ph)C(SiMe₃) (C₅H₄N-2)}Ge-M(η⁵-C₅H₅)(CO)₃] (M = Mo (76), W (77)) --- p.20 / Chapter 1.2.2.1 --- Synthesis of Heteroleptic Germylene [{N(SiMe₃)C(Ph)C- (SiMe₃)(C₅H₄N-2)}Ge(η¹-C₅H₅)] (78) --- p.25 / Chapter 1.2.2.2 --- Spectroscopic Properties of [{N(SiMe₃)C(Ph)C(SiMe₃)- (C₅H₄N-2)}Geη¹-C₅H₅)] (78) --- p.25 / Chapter 1.2.2.3 --- Molecular Structures of [{N(SiMe₃)C(Ph)C(SiMe₃)- (C₅H₄N-2)}Ge(η¹-C₅H₅)] (78) --- p.26 / Chapter 1.2.3.1 --- Synthesis of Germanium(II)-Borane Adduct Adduct Adduct [{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)}Ge(Cl)→(B(C₆H₅)₃)] (79) --- p.29 / Chapter 1.2.3.2 --- Spectroscopic Properties of Germanium(II)-Borane Adduct Adduct [{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)}Ge(Cl)→(B(C₆H₅)₃)](79) --- p.29 / Chapter 1.2.3.3 --- Molecular Structures of Germanium(II)-Borane Adduct Adduct [{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)}Ge(Cl)→(B(C₆H₅)₃)](79) --- p.30 / Chapter 1.2.4.1 --- Synthesis of Pyridyl-1-azaallyl Group 13 Metal Complexes from the Ligand Transfer Reaction between Pyridyl-1-azaallyl Germanium(II) Chloride and Group 13 Metal Halides --- p.34 / Chapter 1.2.4.2 --- Spectroscopic Properties of [{N(SiMe₃)C(Ph)C(SiMe₃)- (C₅H₄N-2)}GaCl₂] (80) and [{N(SiMe₃)C(Ph)C(SiMe₃)- (C₅H₄N-2)}₂InCl] (81) --- p.35 / Chapter 1.2.4.3 --- Molecular Structures of [{N(SiMe₃)C(Ph)C(SiMe₃)- (C₅H₄N-2)}GaCl₂] (80) and [{N(SiMe₃)C(Ph)C(SiMe₃)- (C₅H₄N-2)}₂InCl] (81) --- p.36 / Chapter 1.2.5.1 --- Hydrolysis of Pyridyl-1-azaallyl Germanium(II) Chloride with Water --- p.40 / Chapter 1.2.5.2 --- Spectroscopic Properties of [{HNC(Ph)CH(C₅H₄N-2)}GeCl] (82) --- p.40 / Chapter 1.2.5.3 --- Molecular Structure of [{HNC(Ph)CH(C₅H₄N-2)}GeCl] (82) --- p.41 / Chapter 1.3 --- Experimental for Chapter 1 --- p.43 / Chapter 1.4 --- References for Chapter 1 --- p.49 / Chapter Chapter 2 --- Synthesis and Reactivity Study of Pyridyl-1-azaallyl Germanium(I) Dimer / Chapter 2.1 --- Introduction --- p.55 / Chapter 2.1.1 --- General Aspects of Digermynes and Germanium(I) Dimers Supported by Bulky Ligands --- p.55 / Chapter 2.1.2 --- Objectives --- p.67 / Chapter 2.2 --- Results and Discussion --- p.69 / Chapter 2.2.1.1 --- Reduction of Pyridyl-1-azaallyl Germanium(II) Chloride:Synthesis of Germanium(I) Dimers [C(Ph)C(SiMe₃)- (C₅H₄N-2)]₂Ge₂ (111) and [N(SiMe₃)C(Ph)C(SiMe₃)- (C₅H₄N-2)]₂Ge₂ (112) --- p.69 / Chapter 2.2.1.2 --- Spectroscopic Properties of [N(SiMe₃)C(Ph)C(SiMe₃)- (C₅H₄N-2)Mg(μ-Cl)(THF)]₂ (110), [C(Ph)C(SiMe₃)- (C₅H₄N-2)]₂Ge₂ (111) and [N(SiMe₃)C(Ph)C(SiMe₃)- (C₅H₄N-2)]₂Ge₂ (112) --- p.71 / Chapter 2.2.1.3 --- Molecular Structures of [N(SiMe₃)C(Ph)C(SiMe₃)- (C₅H₄N-2)Mg(μ-Cl)(THF)]₂(110), [C(Ph)C(SiMe₃)- (C₅H₄N-2)]₂Ge₂ (111) and [N(SiMe₃)C(Ph)C(SiMe₃)- (C₅H₄N-2)]₂Ge₂ (112) --- p.72 / Chapter 2.2.2.1 --- Synthesis of [PhNGe{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)}]₂ (113) --- p.80 / Chapter 2.2.2.2 --- Spectroscopic Properties of [PhNGe{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)}]₂ (113) --- p.80 / Chapter 2.2.2.3 --- Molecular Structure of [PhNGe{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)}]₂ (113) --- p.80 / Chapter 2.2.3.1 --- Synthesis of [{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)(Fe(CO)4)- Ge-Ge{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)}] (114) and [{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)(Fe(CO)4)Ge]₂ (115) --- p.84 / Chapter 2.2.3.2 --- Spectroscopic Properties of [{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)(Fe(CO)₄)- Ge-Ge{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)}](114) and [{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)(Fe(CO)₄)Ge]₂ (115) --- p.86 / Chapter 2.2.3.3 --- Molecular Structures of [{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)(Fe(CO)₄)- Ge-Ge{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)}](114) and [{N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)(Fe(CO)₄)Ge]₂ (115) --- p.87 / Chapter 2.2.4.1 --- Synthesis of the First Germanium Analogue of a Dithiocarboxylic Acid Anhydride: [Ge(S){N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)}]₂S (117) --- p.90 / Chapter 2.2.4.2 --- Spectroscopic Properties of [Ge(S){N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)}]₂S (117) --- p.91 / Chapter 2.2.4.3 --- Molecular Structure of [Ge(S){N(SiMe₃)C(Ph)C(SiMe₃)(C₅H₄N-2)}]₂S (117) --- p.92 / Chapter 2.3 --- Experimental for Chapter 2 --- p.95 / Chapter 2.4 --- References for Chapter 2 --- p.103 / Chapter Chapter 3 --- Synthesis and Characterization of Iminophosphoranyl Methanide Metal Complexes and Group 14 Metallavinylidenes / Chapter 3.1 --- Introduction --- p.109 / Chapter 3.1.1 --- A General Review of Phosphoranoimine Ligands --- p.109 / Chapter 3.1.2 --- A General Review of Group 14 Metal Complexes Containing Phosphoranoimine Ligands --- p.117 / Chapter 3.1.3 --- Objectives --- p.124 / Chapter 3.2 --- Results and Discussion --- p.126 / Chapter 3.2.1.1 --- Synthesis of Heteroleptic Chlorogermylene [{(C₅H₄N-2)C(SiMe₃)P(Ph)₂N(SiMe₃)}GeCl (189) and Chlorostannylene [{(C₅H₄N-2)C (SiMe₃)P(Ph)₂N(SiMe₃)}SnCl] (190) --- p.126 / Chapter 3.2.1.2 --- Spectroscopic Properties of [{(C₅H₄N-2)C(SiMe₃)P(Ph)₂N(SiMe₃)}GeCl (189) and Chlorostannylene [{(C₅H₄N-2)C (SiMe₃)P(Ph)₂N(SiMe₃)}SnCl] (190) --- p.127 / Chapter 3.2.1.3 --- Molecular Structures of [{(C₅H₄N-2)C(SiMe₃)P(Ph)₂N(SiMe₃)}GeCl (189) and Chlorostannylene [{(C₅H₄N-2)C (SiMe₃)P(Ph)₂N(SiMe₃)}SnCl] (190) --- p.128 / Chapter 3.2.2.1 --- Synthesis of Bis(iminophosphoranyl) Germanium(II) Compounds [{H₂C(PPh₂=NSiMe₃)₂}(GeCl₂)] (191) and [HC(PPh₂=N- SiMe₃)₂Ge(η¹-C₅H₅)] (192) --- p.132 / Chapter 3.2.2.2 --- Spectroscopic Properties of [{H₂C(PPh₂=NSiMe₃)₂}(GeCl₂)] (191) and [HC(PPh₂=NSiMe₃)₂Ge(η¹-C₅H₅)] (192) --- p.133 / Chapter 3.2.2.3 --- Molecular Structures of [{H₂C(PPh₂=NSiMe₃)₂}(GeCl₂)] (191) and [HC(PPh₂=NSiMe₃)₂Ge(η¹-C₅H₅)] (192) --- p.134 / Chapter 3.2.3.1 --- Synthesis of Magnesium and Lithium Methanide Complexes [Mg{CH(PPh₂)(PPh₂=NSiMe₃)}₂] (193) and [Li{CH(PPh₂)- (PPh₂=NSiMe₃)}(THF)₂] (194) --- p.139 / Chapter 3.2.3.2 --- Spectroscopic Properties of [Mg{CH(PPh₂)(PPh₂=NSiMe₃)}₂] (193) and [Li{CH(PPh₂)- (PPh₂=NSiMe₃)}(THF)₂] (194) --- p.140 / Chapter 3.2.3.3 --- Molecular Structures of [Mg{CH(PPh₂)(PPh₂=NSiMe₃)}₂] (193)and [Li{CH(PPh₂)- (PPh₂=NSiMe₃)}(THF)₂] (194) --- p.141 / Chapter 3.2.4.1 --- Synthesis of Phosphine-Stabilized Germavinylidene [{(PPh₂=NSiMe₃)(PPh₂)C=Ge:}{(PPh₂=NSiMe₃)(PPh₂)C}₂Ge→Ge:] (195) --- p.145 / Chapter 3.2.4.2 --- Spectroscopic Properties of [{(PPh₂=NSiMe₃)(PPh₂)C=Ge:}{(PPh₂=NSiMe₃)(PPh₂)C}₂Ge→Ge:] (195) --- p.146 / Chapter 3.2.4.3 --- Molecular Structure of [{(PPh₂=NSiMe₃)(PPh₂)C=Ge:}{(PPh₂=NSiMe₃)(PPh₂)C}₂Ge→Ge:] (195) --- p.146 / Chapter 3.2.5.1 --- Synthesis of Phosphine-Stabilized Stannavinylidene [{(PPh₂=NSiMe₃)(PPh₂)C=Sn:}{(PPh₂=NSiMe₃)(PPh₂)C=Sn→ Fe(CO)₄}] (197) --- p.151 / Chapter 3.2.5.2 --- Spectroscopic Properties of [Sn{{471}²-C(PPh₂=NSiMe₃)(PPh₂)}](196) and [{(PPh₂=NSiMe₃)(PPh₂)C=Sn:}{(PPh₂=NSiMe₃)(PPh₂)C=Sn→Fe(CO)₄}] (197) --- p.152 / Chapter 3.2.5.3 --- Molecular Structures of [Sn{{471}²-C(PPh₂=NSiMe₃)(PPh₂)}] (196) and [{(PPh₂=NSiMe₃)(PPh₂)C=Sn:}{(PPh₂=NSiMe₃)(PPh₂)C=Sn→Fe(CO)₄}] (197) --- p.157 / Chapter 3.2.6.1 --- Synthesis of 1, 3-diplumbacyclobutane [Pb{{471}²-C(PPh₂=NSiMe₃)- (PPh₂)}]₂ (200) derived from iminophosphoranyl phosphine --- p.163 / Chapter 3.2.6.2 --- Spectroscopic Properties of [Pb{{471}²-C(PPh₂=NSiMe₃)- (PPh₂)}]₂ (200) --- p.164 / Chapter 3.2.6.3 --- Molecular Structure of [Pb{{471}²-C(PPh₂=NSiMe₃)- (PPh₂)}]₂ (200) --- p.164 / Chapter 3.3 --- Experimental for Chapter 3 --- p.167 / Chapter 3.4 --- References for Chapter 3 --- p.176 / Chapter Chapter 4 --- Conclusion / Chapter 4.1 --- Conclusion --- p.186 / Chapter 4.1.1 --- Reactivity Study of Pyridyl-1-azaallyl Germanium(II) Chloride --- p.186 / Chapter 4.1.2 --- Synthesis and Reactivity Study of Pyridyl-1-azaallyl Germanium(I) Dimer --- p.187 / Chapter 4.1.3 --- Synthesis and Characterization of Iminophosphoranyl Methanide Metal Complexes and Group 14 Metallavinylidenes --- p.191 / Chapter 4.2 --- References for Chapter 4 --- p.193 / Chapter Appendix I / Chapter A. --- General Procedures --- p.194 / Chapter B. --- Physical and Analytical Measurements --- p.194 / Chapter Appendix II / Chapter Table A.1. --- Selected Crystallographic Data for Compounds 76-79 --- p.197 / Chapter Table A.2. --- Selected Crystallographic Data for Compounds 80-82 and 110 --- p.198 / Chapter Table A.3. --- Selected Crystallographic Data for Compounds 111-114 --- p.199 / Chapter Table A.4. --- Selected Crystallographic Data for Compounds 117 and 118-191 --- p.200 / Chapter Table A.5. --- Selected Crystallographic Data for Compounds 192-195 --- p.201 / Chapter Table A.6. --- Selected Crystallographic Data for Compounds 196-197 and 200 --- p.202

While games can be an innovative and a highly promising approach to education, creating effective educational games is a challenge. It requires effectively integrating educational content with game attributes and aligning cognitive and affective outcomes, which can be in conflict with each other. Intelligent Tutoring Systems (ITS), on the other hand, have proven to be effective learning environments that are conducive to strong learning outcomes. Direct comparisons between tutoring systems and educational games have found digital tutors to be more effective at producing learning gains. However, tutoring systems have had difficulties in maintaining students€™ interest and engagement for long periods of time, which limits their ability to generate learning in the long-term. Given the complementary benefits of games and digital tutors, there has been considerable effort to combine these two fields. This dissertation undertakes and analyzes three different ways of integrating Intelligent Tutoring Systems and digital games. We created three game-like systems with cognition, metacognition and affect as their primary target and mode of intervention. Monkey's Revenge is a game-like math tutor that offers cognitive tutoring in a game-like environment. The Learning Dashboard is a game-like metacognitive support tool for students using Mathspring, an ITS. Mosaic comprises a series of mini-math games that pop-up within Mathspring to enhance students' affect. The methodology consisted of multiple randomized controlled studies ran to evaluate each of these three interventions, attempting to understand their effect on students€™ performance, affect and perception of the intervention and the system that embeds it. Further, we used causal modeling to further explore mechanisms of action, the inter-relationships between student€™s incoming characteristics and predispositions, their mechanisms of interaction with the tutor, and the ultimate learning outcomes and perceptions of the learning experience.

The dissertation is organized into two main parts. The first part considers fractal extension operators. Although extension operators are available for general subsets of Euclidean domains or metric spaces, our extension operator is unique in that it utilizes both the iterative nature of the fractal and finite element approximations to construct the operator. The resulting operator is especially well suited for future numerical work on domains with prefractal boundaries. In the dissertation we prove the existence of a linear extension operator, Π from the space of Hölder continuous functions on a fractal set S to the space of Hölder continuous functions on a larger domain Ω. Moreover this same extension operator maps functions of finite energy on the fractal to H1 functions on the larger domain Ω. In the second part, we consider boundary value problems in domains with fractal boundaries. First we consider the Sierpinski prefractal and how we might apply the technique of singular homogenization to thin layers constructed on the prefractal. We will also discuss numerical approximation in domains with fractal boundaries and introduce a finite element mesh developed for studying problems in domains with prefractal Koch boundaries. This mesh exploits the self-similarity of the Koch curve for arbitrary rational values of α and its construction is crucial for future numerical study of problems in domains with prefractal Koch curve boundaries. We also show a technique for mesh refinement so that singularities in the domain can be handled and present sample numerical results for the transmission problem.

Educational games intend to make learning more enjoyable, but at the potential cost of compromising learning efficiency. Therefore, instead of creating educational games, we create learning environment with game-like elements: the elements of games that are engaging. Our approach is to assess each game-like element in terms of benefits such as enhancing engagement as well as its costs such as sensory or working memory overload, with a goal of maximizing both engagement and learning. We developed different four versions of a math tutor with different degree of being game-like such as adding narrative and visual feedback. Based on a study with 297 students, we found that students reported more satisfaction with more 'game-like' tutor but we were not able to detect any conclusive difference in learning among the different tutors. We collected student data of various types such as their attitude and enjoyment via surveys, performance within tutor via logging, and learning as measured by a pre/post-test. We created a causal model using software TETRAD and contrast the causal modeling approach to the results we achieve with traditional approaches such as correlation matrix and multiple regression. Relative to traditional approaches, we found that causal modeling did a better job at detecting and representing spurious association, and direct and indirect effects within variables. Causal model, augmented with domain knowledge about likely causal relationships, resulted in much more plausible and interpretable model. We propose a framework for blending exploratory results from causal modeling with randomized controlled studies to validate hypotheses.

Comparative genomic studies have identified noncoding regions of the genome which are often more highly conserved between species than protein-coding sequences. One possible explanation for this conservation of non-coding sequences is some form of selective constraint since sequence conservation at great evolutionary depths is a preliminary indication of functional constraint. Here, I consider nearly 2500 putative regulatory elements, termed Conserved Noncoding Elements (CNEs), that are conserved across seven vertebrate species (human, macaque, mouse, chicken, frog, zebrafish and fugu). I distinguish between CNEs that show accelerated rates of evolution and those that have remained more constrained throughout evolution, and identify CNEs that show higher than expected substitution rates in the human lineage that may be potential candidates of adaptive evolution. However, it is not trivial to demonstrate the action of selection on such sequences. It is relatively easier in the case of protein-coding DNA, since selection would be predicted to result in different rates of substitution for synonymous and non-synonymous sites. Hence, I use the same seven species to define phylogenetically invariant positions in CNEs in contrast to those that have at least one substitution and analyse them independently to determine if there is a positive correlation between evolutionary conservation and the strength of purifying selection at individual sites. In the 1000 Genomes, but not the HapMap, data I find a significant excess of rare derived alleles in CNEs relative to coding sequences. This excess of rare alleles can be best explained if selection is relatively consistent across sites, with most mutations resulting in a similar reduction in fitness. Finally, I explore patterns of variation in the allele-frequencies within human populations, however do not detect any significant differences in the underlying distribution of negatively selected variants among human populations.

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Thesis. 1978. Ph.D. cn--Massachusetts Institute of Technology. Dept. of Chemistry. / Includes bibliographical references. / Ph.D.cn

O trabalho tem como objetivo a utilização do método dos elementos finitos para o cálculo da durabilidade de componentes mecânicos. Para isso, foi desenvolvido um estudo de caso que contempla, passo a passo, a metodologia utilizada. Um conjunto knuckle assembly dianteiro de um veículo off-road, fornecido por uma montadora nacional foi utilizado no estudo de caso. A geometria foi discretizada e modelada em software de pré-processamento em elementos finitos, o MSC.Patran®. Em seguida, foi submetida à análise estática no solver MSC.Nastran® para enfim obter-se o cálculo de durabilidade através do solver Fatigue®. Uma extensa revisão teórica foi realizada a fim de que o estudo tivesse embasamento teórico. / The work has as objective the use of the finite elements method for the calculation of the components durability. A case study using the proposal methodology was developed. A front set knuckle assembly of an off-road vehicle, supplied by a national assembly company was used in the case study. Geometry was discretized and shaped in software of pre-processing in finite elements, the MSC.Patran®. After that, it was submitted to the static analysis using the solver MSC.Nastran®, and the durability calculation using the solver Fatigue®. An extensive theoretical revision was carried through so that the study had theoretical basement.