We prove various results in additive combinatorics for subsets of random sets. In particular we extend Sarkozy's theorem and a theorem of Green on long arithmetic progressions in sumsets to dense subsets of random sets with asymptotic density 0. Our proofs require a transference argument due to Green and Green-Tao which enables us to apply known results for sets of positive upper density to subsets of random sets which have positive relative density. We also prove a density result which states that if a subset of a random set has positive relative density, then the sumset of the subset must have positive upper density in the integers.

We prove various results in additive combinatorics for subsets of random sets. In particular we extend Sarkozy's theorem and a theorem of Green on long arithmetic progressions in sumsets to dense subsets of random sets with asymptotic density 0. Our proofs require a transference argument due to Green and Green-Tao which enables us to apply known results for sets of positive upper density to subsets of random sets which have positive relative density. We also prove a density result which states that if a subset of a random set has positive relative density, then the sumset of the subset must have positive upper density in the integers.

We prove various results in additive combinatorics for subsets of random sets. In particular we extend Sarkozy's theorem and a theorem of Green on long arithmetic progressions in sumsets to dense subsets of random sets with asymptotic density 0. Our proofs require a transference argument due to Green and Green-Tao which enables us to apply known results for sets of positive upper density to subsets of random sets which have positive relative density. We also prove a density result which states that if a subset of a random set has positive relative density, then the sumset of the subset must have positive upper density in the integers. / Science, Faculty of / Mathematics, Department of / Graduate

The objective of this research was to develop a system to effectively monitor temperature in the selective laser melting of Inconel 625. This study established a monitoring system that collects temperature data and describes its relationship with process parameters, develops a control simulation based on the obtained results and determines how to change input parameters in situ. Such research was driven by the unreliability of additively manufactured components, which often contain internal voids and cracks as well as display poor surface finish. With the need for improved part quality, a temperature monitoring system, a promising method of solving several quality issues, proves necessary. This monitoring system was developed using a pyrometer and a thermal imager mounted on a powder bed metal printer to record the peak temperature of the melt pool. Experiments found that both laser power and scan speed affect the peak melt pool temperature of Inconel 625: as the peak melt pool increases as power increases and as scan speed decreases. A subset of experiments run with a thermal camera further revealed that there is no discernible temperature trend across the laser track, meaning that there was no significant difference in temperature at the start, middle or end of the track. The thermal camera also revealed that temperature across the melt pool resembled a second order response to laser input. Furthermore, according to preliminary offline measurements taken of the primary dendrite arm spacing (PDAS) of Inconel 625 coupons, PDAS increases with peak temperature. In addition to implementing and testing the monitoring system, this research created and simulated a first order model of the system using a discreet proportional integral derivative controller. Lastly, two separate methods were found to interface a controller with the Omnisint 160 in order to change the laser power based on the temperature feedback / Thesis / Master of Applied Science (MASc)

For additive manufacturing, research has shown that the chemistry and microstructural properties of the feedstock powder can significantly affect the properties of the consolidated material. Thermal treatment and recycling parameters for powders used in both solid and liquid state processes can further affect the microstructure and properties of the consolidated parts. Understanding the powder microstructure and effects of powder pre-treatment can aid in optimizing the properties of the final consolidated part. This research proposes a method for the characterization and optimization of powder pre-processing thermal parameters using aluminum alloy powder as examples. Light microscopy, electron microscopy, and hardness were used to evaluate each condition.

In this study, Effect of Molybdenum disulfide (MoS2), Anglamol(SP) and Tricresyl phosphate(TCP) additives on the tribological performance of loosing and tightening process of screw and nut were investigated by using a self-developed tribological tester. The screw and nut are made of SCM 440 and HBsC3, respectively. Result shows that the MoS2 additives with Grease#0 give the best tribological performance but TCP with Grease#0 is worst. With increasing concentration of MoS2 , the lubricant life increases, reaches a maximum at about 5wt% and finally diminishes with decreasing. Surface pressure between the screw and nut, the lubricant life increases. Under the surface pressure of 2.64kg/mm2, the lubricant life can achieve 8000 cycles or more. To maintain the long life of the screw and nut, the surface pressure should be equal to or less than 2.64kg/mm2.

The simultaneous separation of anionic and cationic proteins has been achieved by addition of high concentration of poly(diallyldimethylammonium chloride) (PDDAC) in capillary electrophoresis. A capillary was filled with PDDAC so that it would act as ion-pair reagents in the separation of anionic proteins. On the other hand, the PDDAC can also be used as coating additives for the analysis of cationic proteins. Increasing the concentration of PDDAC in the separation buffer had the ability to improve the separation efficiency, change the electrophoretic mobility, and alter the separation selectivity; however, this was not true in the case of analyzing proteins by using the PDDAC larger than 1.6%. By both using a buffer containing 1.6% PDDAC and applying pH-stepwise techniques, 13 proteins with a wide range of pI (4.7¡V11.1) and molecular masses (6.5¡V198.0 kDa) could be separated within 30 min in a single run. In addition to this separation, we observed notonly more peaks from alph-chymotrypsinogen A and aprotinin but also the bovine serum albumin (BSA) dimer and trimer. The second part describes a method for enrichment and separation of acidic and basic proteins using the centrifugal ultrafiltration followed by polyelectrolyte-filled capillary electrophoresis. In order to improve stacking and separation efficiencies of proteins, the separation buffer containing 1.6% poly(diallyldimethylammonium chloride) was added with gold nanoparticles (AuNPs), poly(ethylene oxide), cetyltrimethyl ammonium bromide, and poly(vinyl alcohol). As a result, the use of AuNPs as additives exhibited better efficiency in separation, stacking and analysis time. Even for large-volume samples (110 nL), the separation efficiencies of acidic and basic proteins remained greater than 104 and 105 plates/m, respectively. To further enhance detection sensitivity, protein samples were enriched using the centrifugal ultrafiltration, followed by our proposed stacking method. As a result, the detection sensitivity was improved up to 314-fold as compared with normal hydrodynamic injection. Additionally, the limits of detection at a signal-to-noise of 3 for most proteins are down to nanomolar range. We have validated the application of our method by means of analyses of 50 nM lysozyme in saliva samples. The proposed method was also successfully applied to the analyses of egg-white proteins, which have large differences in molecular weight and pI.

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

No description available.

Thesis (Ph. D.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 257-259).