Thesis advisor: Elida V. Laski / Use of base-10 decomposition strategy for addition in first grade is related to mathematics advantage in the later years (Geary et al., 2013), yet we know little about the strategy’s prevalence among first graders or factors contributing to its use. The present study sought to bridge this gap by testing 87 first graders in the greater Boston area. The results confirmed previous findings that showed that in the last 10 years first graders in the US have increased in frequency of base-10 decomposition. Children who had better knowledge of basic number facts used it more frequently, particularly on problems with smaller addends. Further, the study tested whether an instructional intervention would be effective in increasing reliance on base-10 decomposition. 61 of the original participants were selected to take part in an experimental intervention that taught them to execute the strategy while relying on external representations – sometimes known as manipulatives. Informed by two lines of research, the present study tested the hypothesis that the efficacy of the intervention may depend on whether one or multiple external representations are used for instruction. The results showed a dramatic increase in first graders’ mental base-10 decomposition use as a result of the intervention. Children grew in their use of the strategy at the same rates across genders, levels of basic arithmetic fluency, and working memory. Overall, the results showed that relying on multiple representations during instruction appears more beneficial to strategy use on mental arithmetic, but this benefit may be conditional on how well the children have mastered and abstracted the strategy. Implications to classroom interventions aimed to increase the use of advanced arithmetic strategies are discussed. / Thesis (PhD) — Boston College, 2016. / Submitted to: Boston College. Lynch School of Education. / Discipline: Counseling, Developmental and Educational Psychology.

The research presented herein is concerned with the exploration of rhodium-catalysed addition reactions with organoboranes encompassing the 1,4-addition enolate protonation to benzyl acrylate esters, and the synthesis of chiral organoboranes for use in the synthesis of natural products Hermitamides A and B. Chapter 1 introduces the area of rhodium-catalysed conjugate addition as a tool for asymmetric synthesis. An extensive discussion of this methodology is included and recent advances in the area will be highlighted. In addition to this some recently published alternatives to organoboranes are outlined and their use in rhodium-catalysed chemistry documented. Chapter 2 discusses the tandem process of rhodium-catalysed conjugate addition enolate protonation, a recently observed asymmetric development. By using a novel route to benzyl acrylic esters the synthesis of α,α′-dibenzyl esters is achieved in excellent yields and selectivity. This study highlights the fact that when dealing with 1,1-disubstituted activated alkenes it is more difficult to produce enantioselective results as the chirality is determined in the protonation step and not during insertion. Some insights into the mechanism are proposed based on the outcomes observed. Chapter 3 describes the total synthesis of Lyngbic Acid and related structures Hermitamides A and B. Synthesis of these natural products are achieved by synthesis of an enantiopure organoborane species and its subsequent coupling via rhodium catalysis. Some interesting insights into the addition of alkenyl organoborane species to unsubstituted 1,1-activated alkenes are detailed. Chapter 4 describes the synthesis and characterisation for the compounds discussed in the previous chapters.

Thesis (Ph.D.)--University of Delaware, 2007. / Principal faculty advisor: James Hiebert, School of Education. Includes bibliographical references.

Field Programmable Gate Arrays (FPGA) are increasingly being used to design high end computationally intense microprocessors capable of handling both fixed and floating-point mathematical operations. Addition is the most complex operation in a floating-point unit and offers major delay while taking significant area. Over the years, the VLSI community has developed many floating-point adder algorithms mainly aimed to reduce the overall latency. An efficient design of floating-point adder onto an FPGA offers major area and performance overheads. With the recent advancement in FPGA architecture and area density, latency has been the main focus of attention in order to improve performance. Our research was oriented towards studying and implementing standard, Leading One Predictor (LOP), and far and close data-path floating-point addition algorithms. Each algorithm has complex sub-operations which lead significantly to overall latency of the design. Each of the sub-operation is researched for different implementations and then synthesized onto a Xilinx Virtex2p FPGA device to be chosen for best performance. This thesis discusses in detail the best possible FPGA implementation for all the three algorithms and will act as an important design resource. The performance criterion is latency in all the cases. The algorithms are compared for overall latency, area, and levels of logic and analyzed specifically for Virtex2p architecture, one of the latest FPGA architectures provided by Xilinx. According to our results standard algorithm is the best implementation with respect to area but has overall large latency of 27.059 ns while occupying 541 slices. LOP algorithm improves latency by 6.5% on added expense of 38% area compared to standard algorithm. Far and close data-path implementation shows 19% improvement in latency on added expense of 88% in area compared to standard algorithm. The results clearly show that for area efficient design standard algorithm is the best choice but for designs where latency is the criteria of performance far and close data-path is the best alternative. The standard and LOP algorithms were pipelined into five stages and compared with the Xilinx Intellectual Property. The pipelined LOP gives 22% better clock speed on an added expense of 15% area when compared to Xilinx Intellectual Property and thus a better choice for higher throughput applications. Test benches were also developed to test these algorithms both in simulation and hardware. Our work is an important design resource for development of floating-point adder hardware on FPGAs. All sub components within the floating-point adder and known algorithms are researched and implemented to provide versatility and flexibility to designers as an alternative to intellectual property where they have no control over the design. The VHDL code is open source and can be used by designers with proper reference.

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Polypropionates represent a large family of natural products and several strategies have been developed for their synthesis. The aldol reaction is one of the most important tools for the construction of polypropionate natural products. The Ward group has developed an approach to polypropionate natural products based on sequential aldol reactions of thiopyran building blocks. The Thiopyran Route to Polypropionates (TR2P) involves the stepwise aldol reactions of 15 and 16 to rapidly access stereochemically complex tetrapropionate and hexapropionate synthons in a few steps. The current work describes the effort to prepare enantioenriched 17-AA and/or 17-SA through chiral transition metal based Lewis acids (176) and chiral organocatalysts (48, 179) with chelating Lewis acids. The preparation of non-Felkin tetrapropionate and hexapropionate synthons through the use of a weak base in conjunction with a Lewis acid was developed.

AIM: The primary purpose of this thesis was to evaluate the pattern of changes to accommodation and phoria when pre-presbyopic individuals perform near work for 20 minutes with +2D lenses. In addition, the thesis also investigates the effect of the accommodative vergence cross-link (AV/A) and age on binocular adaptation to addition lenses. METHODS: Accommodation was measured using the PowerRefractor (Multichannel Systems, Germany) and phoria was measured using the modified Thorington Technique. Twenty four pre-presbyopic and emmetropic individuals (11 adults and 13 children) participated in the study. All participants fixated a near target at a distance of 33 cm for 20 minutes with +2D (lens condition) and without (no lens condition) +2D addition lenses. Binocular and monocular changes in accommodation and near phoria were measured at the outset and at 3, 6, 9, 15 and 20 minute intervals. RESULTS: Effect of +2D lenses on accommodation and phoria: The emmetropic adult participants exhibited lag of accommodation under the no lens condition (binocular: 0.51 ± 0.12D; monocular: 0.64 ± 0.15D) that were eliminated (under monocular viewing) and reversed (exceeded demand by 0.51 ± 0.11 D under binocular viewing condition) with the addition of +2D lenses. The near phoria showed a significant increase towards exophoria by 6 ± 0.56 ∆D upon introduction of +2D lenses. Sustained near viewing with +2 D lenses resulted in significant reduction of the binocular focus alone (not monocular focus) after 3 minutes of binocular viewing (magnitude of reduction: 0.24D; P<0.01). The exophoria also showed a concomitant reduction after 3 minutes of fixation at the near task (Magnitude of reduction: 3.6 ± 0.6 ∆D; P<0.001). The magnitude and rate of vergence adaptation, determined using an exponential function, was found to be 4.6 ± 0.21 ∆D and 2.12 minutes respectively for the emmetropic adult participants. Effect of age on vergence adaptation: A pattern of significant reduction in phoria and binocular focus similar to the adult participants was observed in young children. Analysis of the vergence adaptation curves in the two age groups did not show any significant difference in both the magnitude as well as the rate of phoria adaptation within the age range tested (Magnitude of adaptation - Adults: 4.65 ∆D; Children: 4.51 ∆D; P > 0.05; Time constants -Adults: 2.12 minutes: Children: 1.53 minutes, P > 0.05). Effect of AV/A ratio on vergence adaptation: The stimulus (St-AV/A) and the response AV/A (R-AV/A) ratios were determined and the participants were divided into two groups (low and high AV/A ratio) under both the conditions. The result indicated that, under both testing conditions (stimulus and response AV/A), the individuals with higher AV/A ratios demonstrated greater magnitudes of vergence adaptation than those individuals with lower ratios (Magnitude of adaptation: Low St-AV/A = 4.12 ∆D; Low R-AV/A= 4.25∆D; High St-AV/A = 4.88 ∆D; High R-AV/A = 4.65∆D; P<0.05) CONCLUSIONS: Introduction of near addition lenses initiated an increase in exophoria and convergence driven accommodation. Vergence adaptation occurred after 3 minutes of binocular viewing thus reducing exophoria and convergence driven accommodation. The magnitude and completeness of phoria adaptation were seen to depend on an individuals AV/A ratio with greater magnitude and incomplete adaptation observed in participants with higher AV/A ratios. Age, within the limits of the study did not appear to influence phoria adaptation with near addition lenses.

Field Programmable Gate Arrays (FPGA) are increasingly being used to design high end computationally intense microprocessors capable of handling both fixed and floating-point mathematical operations. Addition is the most complex operation in a floating-point unit and offers major delay while taking significant area. Over the years, the VLSI community has developed many floating-point adder algorithms mainly aimed to reduce the overall latency. An efficient design of floating-point adder onto an FPGA offers major area and performance overheads. With the recent advancement in FPGA architecture and area density, latency has been the main focus of attention in order to improve performance. Our research was oriented towards studying and implementing standard, Leading One Predictor (LOP), and far and close data-path floating-point addition algorithms. Each algorithm has complex sub-operations which lead significantly to overall latency of the design. Each of the sub-operation is researched for different implementations and then synthesized onto a Xilinx Virtex2p FPGA device to be chosen for best performance. This thesis discusses in detail the best possible FPGA implementation for all the three algorithms and will act as an important design resource. The performance criterion is latency in all the cases. The algorithms are compared for overall latency, area, and levels of logic and analyzed specifically for Virtex2p architecture, one of the latest FPGA architectures provided by Xilinx. According to our results standard algorithm is the best implementation with respect to area but has overall large latency of 27.059 ns while occupying 541 slices. LOP algorithm improves latency by 6.5% on added expense of 38% area compared to standard algorithm. Far and close data-path implementation shows 19% improvement in latency on added expense of 88% in area compared to standard algorithm. The results clearly show that for area efficient design standard algorithm is the best choice but for designs where latency is the criteria of performance far and close data-path is the best alternative. The standard and LOP algorithms were pipelined into five stages and compared with the Xilinx Intellectual Property. The pipelined LOP gives 22% better clock speed on an added expense of 15% area when compared to Xilinx Intellectual Property and thus a better choice for higher throughput applications. Test benches were also developed to test these algorithms both in simulation and hardware. Our work is an important design resource for development of floating-point adder hardware on FPGAs. All sub components within the floating-point adder and known algorithms are researched and implemented to provide versatility and flexibility to designers as an alternative to intellectual property where they have no control over the design. The VHDL code is open source and can be used by designers with proper reference.

Conjugate addition reactions are one of the most widely used carbon-carbon bond forming reactions in organic synthesis. This reaction can form a chiral center and can be used for the synthesis of structurally complex compounds. Until now it has been necessary to use a chiral heavy metal catalyst in order to carry out asymmetric addition of aromatic groups to α,b-unsaturated enones via conjugate addition. Recently we have been successful in achieving the same task using an arylboronate as well as a catalytic amount of a chiral substituted binaphthol (BINOL). Using this reaction method great yields and enantioselectivities were achieved when diethyl phenylboronate was added to various enones and when various diethyl arylboronates were added to chalcone. This reaction is exciting because it eliminates the chance of having trace amounts of heavy metals in the final product, which is advantageous in such areas as the pharmaceutical industry.

Conjugate addition reactions are one of the most widely used carbon-carbon bond forming reactions in organic synthesis. This reaction can form a chiral center and can be used for the synthesis of structurally complex compounds. Until now it has been necessary to use a chiral heavy metal catalyst in order to carry out asymmetric addition of aromatic groups to α,b-unsaturated enones via conjugate addition. Recently we have been successful in achieving the same task using an arylboronate as well as a catalytic amount of a chiral substituted binaphthol (BINOL). Using this reaction method great yields and enantioselectivities were achieved when diethyl phenylboronate was added to various enones and when various diethyl arylboronates were added to chalcone. This reaction is exciting because it eliminates the chance of having trace amounts of heavy metals in the final product, which is advantageous in such areas as the pharmaceutical industry.