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- PublicationRestrictedRiemann integration(1996)Seng, Wendy Gek Cheng
Show more The Riemann integration is well-known. It is also well-known that if a sequence of Riemann I ntegrable functions converges uniformly to a limit function, then the limit function is also Riemann integrable. However, there are other convergence theorems for the Riemann integral, some of which were not so well-known and some were even discovered recently. We shall look into few such convergence theorems.Show more 154 17 - PublicationRestrictedA study on the general levels of heavy metals in magazines and a comparative study of microwave and ultrasound acid digestions(1996)Yeo, Joyce Suat Peng
Show more This study has been undertaken to determine the general levels of some toxic metals in magazines. The objective of this work was to initiate and stimulate the study of heavy metals due to coloured pigments as well as that of magazines as a whole. The concentration of three toxic metals were determined by atomic absorption method using standard solutions for calibrations. Microwave digestion was employed to release the trace metals into the acid. The results show that three colours in local magazines contain high level of Pb ranging from 1.6 μg/g to 59.0 μg/g. Cr appeared somewhat lower which recorded between 0.4 and 16.1 μg/g. The range of Cd falls between 0 and 7.4 μg/g. The mean total Pb, Cr and Cd concentrations of the various magazines are as high as 12.85, 8.89 and 0.91 mg per copy respectively. These multiplied by their annual sales volume thus indicate that magazine disposal is a source of environmental pollution.

A preliminary study is also undertaken to compare microwave and ultrasound digestion using magazine and paint flakes. Statistical evaluation by regression treatment was applied and high correlation coefficients at 95% confidence level which indicate the good accuracy and precision of the alternative method compared to the standard microwave digestion.Show more 139 24 - PublicationRestrictedA kinetic analysis of a series of drop jump : the effect of drop height and rest periods(1996)Tang, Yew Seng
Show more This study was composed of three parts with the overall aim being to investigate the effects of drop height and rest period on the kinetic measures associated with the performance of 40 drop jumps, a commonly used stretch-shortening cycle (SSC) activity for the development of strength and power The purpose of Part One was to determine an appropriate drop height from between 40 to 70 cm; Part Two investigated the relationship between the kinetic variables and isokinetic strength and power measures and functional estimates of muscular power; and Part Three investigated the effect of a one minute rest between each set of ten drop jumps on the kinetic measures of 40 drop jumps.

Eight male subjects aged 18.7 2 0.5 years were selected from a Singapore Junior College track and field team to participate in this study with all subjects considered to be sprint and jump specialists In Part One, subjects performed one set of 10 drop jumps from each of four heights, specifically, 40 cm (DJ40), 50 cm (DJ50), 60 cm (DJ60) and 70 cm (DJ70). The ground contact time, flight time and peak vertical ground reaction forces were measured from a Kistler mobile force platform (Model 9286) with the rebound height being subsequently calculated. Results of paired t-tests revealed no significant difference in the mean rebound height across the four drop heights, however; based on ground contact times and vertical ground reaction forces the use of a 40 to 50 cm drop height was suggested. A drop height of 50 cm was therefore selected as it was thought this would elicit maximal benefits with respect to the SSC movement, while still being considered safe.

Having established the drop height, one week later subjects were requested to complete 40 consecutive drop jumps and one week later again, subjects completed 40 drop jumps with a one minute rest period between each set of ten jumps. Changes in the kinetic variables of coupling time, ground contact time, rebound height, peak vertical ground reaction force, magnitude of first impact spike and angle of knee flexion were measured across the 40 drop jumps for each condition.

The kinetic variables analyzed from the 40 consecutive drop jumps were correlated with the maximum peak torque and average power measurements obtained during a concentric-eccentric knee extension-flexion task on a Cybex 6000 dynamometer at 180 and 240 degrees per second and functional estimates of muscular power (50 m sprint time, vertical jump height and power). Pearson product-moment correlation analysis revealed a positive relationship between the coupling time of the drop jump and the two performance measures of 50 m sprint and vertical jump power, suggesting that subjects may have been using a greater proportion of slow-twitch muscle fibres when performing these activities. In addition, it was suggested that the isokinetic measurements obtained may not be good indicators of drop jump ability.

The final part of this study investigated the effect of a rest period on the kinetic changes across the 40 drop jumps. Changes in the kinetic variables (as measured in Part Two) were analyzed using a MANOVA statistics for the two different treatments across the 40 jumps. A Student's t-test was subsequently used to determine the differences in the kinetic variables between the two treatments.

No significant changes were observed in the kinetic variables measured across the 40 drop jumps in either condition, with no significant difference in the kinetic variables between the two conditions. Despite this, there was a trend of reduced variability in the kinetic measures associated with the drop jump series with one minute rest intervals, compared to the 40 consecutive drop jumps.

In conclusion, this study recommends the use of a 40 to 50 cm drop height when implementing drop jump training. In addition, despite no significant changes being observed in the kinetic variables of interest, the reduced variability observed when the drop jumps were performed with a one minute rest interval, may suggest that this protocol is beneficial in minimizing "undesirable" jumps when performing a series of drop jumps. Lastly, coupling time was found to be closely related to speed and power performance and thus further studies should investigate the possible relationship between coupling time and muscle fibre composition. If a relationship is established between these variables, this simple kinetic measure may be used in preference to the current invasive technique of muscle biopsy for the prediction of muscle fibre composition.Show more 165 20 - PublicationRestrictedCell volume regulation in the intertidal pulmonate, onchidium tumidium(1996)Ho, Soo Yin
Show more Onchidium tumidium is an osmoconformer and that it is able to regulate its volume at 10% or 90% seawater (SW). However, it is a more effective volun2e regulator in 90% SW than in 10% SW. Results indicate that after an upward transfer from 50% to 90% SW, there were significant increases in the total free amino acids (TFAA) in the whole animal, coelomic plasma (CP), body wall (BW) and internal organs (10). Increased proteolysis was more likely to occur in the I0 than in the BW of 0. tumidium exposed to 90% SW as reflected by a lowered water-soluble protein content in the I0 of slugs exposed to 90% SW compared to those of slugs exposed to 50% SW. It is probable that the higher TFAA in the BW of O.tumidium exposed to 90% SW compared to that of slugs exposed to 50% SW was partially due to NH4+ trapping by α-ketoglutarate in the presence of glutamate dehydrogenase to form glutamate as indicated by a significantly higher amination deamination-1 ratio. Glutamate could then be channeled to form other amino acids via transaminases. When being confronted with a downward transfer from 50% SW to 10% SW, there was possibly a release of free amino acids (FAA) from the BW of 0. tumidium into the CP as indicated by the increase in TFAA in the CP and a decrease in TFAA in the BW. The significantly lower amination deamination-1 ratio in the I0 shows that it is most probably involved in the breakdown of FAA during hypoosmotic stress.Show more 139 10 - PublicationRestrictedValidation of the 1600-m run as a predictor of VO2MAX in Singapore children aged 10 to 12 years(1996)Aw Yong, Wai Leng
Show more The purpose of the present study was to determine the validities of the 1600-m run and several anthropometric variables for predicting maximal oxygen uptake (VO2max) in Singapore children aged 10-12 years. Fourteen untrained subjects, 12 boys and 2 girls, performed the 1600-m run on a synthetic track and had VO2max determined in the laboratory. A weak correlation of -0.398 (p > 0.10) was found between VO2max and the 1600-m run time. In fact, subscapular thickness alone has the highest correlation coefficient with VO2max in this group (r = -0.863, p < 0.001). Multiple regression analysis (best-subsets) was conducted and the best predictor variables were height, weight, triceps thickness, subscapular thickness and suprailiac thickness resulting in two prediction equations: (1) VO2max (ml.kg-1.min-1) = 79.9 - 16.6 (height, m) - 0.443 (triceps thickness, mm) -0.902 (subscapular thickness, mm)+ -0.358 (suprailiac thickness, mm), with R2 = 0.864, SEE= 2.189 (p < 0.05). and (2) VO2max (ml.ki1.min-1) = 61.8 - 0.212 (weight, kg) -0.425 (triceps thickness, mm) -0.667 (subscapular thickness, mm) + 0.315 (suprailiac thickness, mm) with R2 = 0.857, SEE = 2.248 (p < 0.05). This study thus suggests that three skinfold sites (triceps, subscapular and suprailiac), height and weight are better predictors ofVO2max than the 1600-m run.Show more 153 12 - PublicationRestrictedKaryological investigation and comparison among tropical lizards (Squamata : Agamidae) and its taxonomic implications(1996)Low, Vivian May Hon
Show more The Family Agamidae (Order: Squamata) in Peninsular Malaysia and Singapore is represented by 7 genera and 25 species of lizards. Nine species of lizards from the 3 genera: Acanthosaura, Calotes, and Gonocephalus, were karyotyped in this study. The karyotypes of five lizards, Acanthosaura armata, Gonocephalus bellii, Gonocephalus liogaster, Gonocephalus chamaeleontinus, and Gonocephalus robinsonii were documented here for the first time. No heteromorphic sex chromosome was evident in the species studied. The karyotypes showed chromosomes of two distinct size groups: macrochromosomes and microchromosomes. The number of macrochrolnosomes within each genus was invariant. Of the 3 genera karyotyped, one genus has diploid numbers more than the ancestral karyotype 2n = 36, while the two other genera had less than the 2n = 36 chromosomes.

Karyological data was used to discuss the taxonomic status of species in the Calotes and Gonocephalus species complex. Calotes cristatellus has a karyotype formula 2n = 34(14M + 20m) while other Calotes species have a karyotype of 2n = 34(12M+20m). In light of the karyological data from this and other published studies, there is justification to reassign Calotes cristatellus to the genus Bronchocela. Karyological results were also used to hypothesize possible modes of speciation of Gonocephalus species on either side of the Wallace line.Show more 150 41 - PublicationRestrictedPower and strength changes following a bout of concentric or eccentric leg press exercise(1996)Chew, Kia Seng
Show more Eccentric muscular actions occur as a result of muscles lengthening during contraction. Previous studies involving such muscular activities have focused on aspects like delayed onset muscle soreness (DOMS), enzyme activity, electrically stimulated muscle characteristics, muscle fibre damage and neuromuscular adaptations (MacIntyre et al., 1995). Although these studies measure physiological components and strength changes, not many researchers have evaluated changes in power after a single intense exercise session.

The present study was designed to measure strength and power following an acute bout of isolated concentric or eccentric leg press exercise. Twenty four subjects (mean age + SD= 23.9 t1.7 years) from the School of Physical Education, Nanyang Technological University were randomly assigned into three groups (n=8). The concentrically exercised (CON) and eccentrically exercised (ECC) groups performed a leg press exercise consisting of 3 sets of 12 repetitions of their maximum isometric strength determined by a modified dynamometer device. Power tests consisted of countermovement jumps (CMJ) and squat jumps (SJ) measured on a force plate, and strength was assessed using isometric leg press dynamometry. Additionally, average peak power and total work on a cycle ergometer for 10 seconds were measured pre-exercise and nine times post exercise. Muscle soreness measurements were made six times pre- and post exercise.

Results revealed greater strength decrements for ECC than CON throughout the study. CMJ heights for both groups show no significant difference (p<.01) and were below baseline even after 48h. SJ heights decreased less than CMJ heights and recovered to baseline by 24h. In peak power and total work, CON recovered to baseline by 2h compared to ECC who recovered by 24h. There was no indication of muscle soreness or DOMS.

Further research needs to be carried out in the area of power changes related to different exercise intensities and muscle groups. Studies should also be designed to examine the relationship of force and velocity in power generation following acute exercise.Show more 120 20 - PublicationRestrictedMolecular analysis of animal tissues for species identification(1996)Chua, Judy Kim Lan
Show more In a multi-racial society, the identity of the consumer meat sold has a great impact on the different religions and races. In this study, various molecular techniques such as restriction endonucleases digestion, rDNA PCR, RAPD PCR and protein PAGE were used on 11 different meat samples were analyzed for species identification. The species of meat samples include chicken, duck, pig, sheep, ostrich, cow, buffalo, kangaroo, horse, wild boar and deer. Differentiation between the different species were based on DNA and protein banding patterns. From the results obtained, it seemed that RAPD PCR was the best method for species identification and differentiation. Restriction endonucleases digestion could be used to identify the species origin of animals, but the quality of the DNA used must be pure and flee from contaminants. For rRNA analysis, comparison between the species can only be done on the same gel, since only one major band is visible under UV light. Protein analysis of the species is easier to perform than the rest of the methods, but due to the close proximity of the bands, species identification and differentiation is difficult. Other than for species identification the same techniques can be used the characterization, construction of genetic and physical maps, forensic casework, wildlife conservation as well as for investigating the relationship between two geographically distinct species. In addition to these techniques, other methods such as FINS, immunological assay and hybridization probes are also used for identification of the origin of the species.Show more 160 21 - PublicationRestrictedA parametric study of the plasma energy of the plasma focus(1996)Tan, Chun Ming
Show more The plasma focus, beside being used as a fusion device, serves as a simple yet cost-effective device to study the fundamentals of pulse technology and plasma physics as a result of a wide range of plasma phenomena arising from this device. Furthermore, the plasma focus can be a source of fusion neutrons and X-rays depending on the working gas used. As these radiations from the focus have many potential uses, it would be useful to optimize these radiations. Although the mechanism concerning the production of radiation is not clear, the process of radiation could be logically deduced to require a store of energy. This project seeks to find the operational parameters for optimization of kinetic energy and energy input into the plasma.Show more 157 30 - PublicationRestrictedSynthesis and preliminary spectroscopic studies into the tautomerism of 3-(arylamino) phthalides(1996)Shah Jahan Mohamed Iqbal
Show more A series of 3-(ary1amino)phthalides of the type RC_{6}H_{4}NH-CHC_{6}H_{4}COO, (R=H; 2-OH; 4-OH; 2-OCH_{3}; 4-OCH_{3}; 2-CH_{3}; 4-CH_{3}; 2-Cl; 4-Cl; 2-NO_{3}; 4-NO_{2}) were synthesized and characterized by 'H, "C NMR and IR spectroscopies. Seven of these phthalides are new compounds.

A convenient method for synthesizing the phthalides is by condensation reaction of 2-formylbenzoic acid with the appropriate substituted aromatic amines in methanol.

IR spectroscopic analysis using KBr disc suggest, in the solid state, that the condensation products exist in the phthalide (closed) form instead of a Schiff base (open form).

'H and^{13}C NMR spectroscopic analysis of the compounds in CDC1, and DMSO-d, confirm that the phthalide form is the predominant form.

In liquid CHCI_{3}, IR spectroscopy was able to detect both the open and close forms of 3-(0-hydroxyani1ino)phthalide and 3-(0-methoxyani1ino)phthalide thus indicating the presence of both ring and chain tautomers. It has been shown qualitatively that these two compounds exist as a form of ring-chain tautomerism with the ring tautomer being more predominant.Show more 157 10 - PublicationRestrictedA diode-pumped Nd : YLF laser(1996)Lee, Chia Hui
Show more Solid state lasers have undergone a renaissance since the development of reliable and cheap laser diodes which can be used as pump sources. This leads to a new class of holosteric lasers which have been demonstrated to be highly efficient, reliable, and are attractive for a wide range of applications. The work described in this academic exercise focuses on the development of a stable gain-switched Nd:YLF laser operating at 1053 nm pumped with a 1.2 W diode array.

A brief history and an overview of diode-pumped solid-state lasers are presented as part of the literature review in the first two chapters. The properties that make LDPSSLs novel and such a fertile field of research are highlighted. Also included are the properties of semiconductor laser diodes and the laser material, Neodynium-doped Yittrium- Lithium- Fluoride.

Chapter three discusses in detail, the general design criterion for the laser setup as well as the rate-equations model which is used as a basis for the simulation program.

In chapter four, the experiments and measurements obtained are presented. The resonator used is a folded, three-mirror cavity resonator in the Fabry-Perot configuration. In this AE, we have demonstrated a diode-pumped Nd:YLF laser operating at 1053 nm in both continuous wave ( CW ) operation and pulsed operation via gain-switching. In the TEM00 operation, the laser produces an maximum output power of 13 mW with a 12.9% transmission output coupler, with a slope efficiency of 1.4%. In the gain-switched operation, generations of single, double and multiple pulses have been observed. These pulses are well simulated by the rate equations model. In the single-pulse generation, pulses of 16 ps duration have been obtained. This is in fairly good agreement with the simulation results which have produced a pulse duration of 12 ps.Show more 135 12 - PublicationRestrictedThe travelling salesman problem(1996)Aliza Main
Show more The Travelling Salesman Problem (TSP) is one of the classic problems in combinatorial optimisation. Its applications arise in problems like the delivery services, customer pick-up services, circuit board drilling, and even in X-ray cryxtallography experiments. As most of these applications involve an open tour, we shall therefore discuss the TSP as one involving an open tour.

TSP basically concerns finding the shortest total distance possible. Since the search for the shortest total distance is not easy to obtain especially when the number of cities is large, lower and upper bounds are introduced to at least find a near-optimal or an optimal solution.

In this paper, we used the Prim's algorithm and a particular heuristic algorithm to compute the lower and upper bounds respectively. We coded these algorithms on FORTRAN 77 so that we could investigate how much the upper bound varies fiom the lower bound. By taking the ratio of the upper bound to the lower bound, we could conduct an investigation on the probability distribution of the percentage of the upper bound exceeding the lower bound for different sets of cities.

Our first attempt at computing the upper and lower bounds shows that the former is on average about 30 percent above the latter, while for certain set of cities it maybe as high as 45 percent above. This percentage indicates that we need to improve the lower bound andlor the upper bound. The implementation of the sub-gadient optimisation method on the lower bound shows a relatively good improvement to 20 percent (maximum 30 percent). However, this can be further improved using a sub-case of the 3-opt algorithm on the upper bound to about 8 percent (maximum 16 percent). Though this 8 percent illustrates that the TSP solution has si@cantly improved, fiuther improvements can still be made by using the 3-opt algorithm or some other heuristic algorithms.Show more 153 21 - PublicationRestrictedThe effect of endurance exercise training on cardiovascular fitness of Singapore primary school children aged 10 to 11 years(1997)Kok, Boon Siang
Show more The purpose of the present study was to investigate the ability of selected Singapore primary school children to improve cardiovascular fitness as indicated by changes in peak oxygen uptake (VO2peak), after a 6-week period of aerobic training on cycle ergometers. 36 children aged 10.8 to 11.7 years were randomly grouped into control (CON) (n = 10 boys and 10 girls) and experimental (EXP) (n = 8 boys and 8 girls) groups. All subjects underwent three 20-minute exercise sessions weekly, at an intensity of 60% of their maximal heart rate (HRmax) Maximal treadmill testing was performed a week before and after training. Female subjects had significantly higher body fat percentage (% BF) but lower VO2peak than the male subjects before and after training (p < .05). VO2peak of the boys and girls were significantly correlated with percentage of body fat (r = -0.58, r = -0.66, p <.05) respectively. Mean VO2peak did not change significantly with training. After training, boys experienced an increase of 2.5 ml/kg/min (5.3%) but girls reported a decrease of 1.6 ml/kg/min (3.8%) (both p > .05). These findings suggested that the intensity of the training program was insufficient to improve the cardiovascular fitness of the selected Singapore primary school children.Show more 142 45 - PublicationRestrictedExtreme value statistics and its applications(1997)Lee, Kok Sonk
Show more An extreme value is the largest or the smallest value in a data set . As n tends to infinity , the largest or the smallest value of a sample size n has asymptotically one of the 3 Types of Extreme Value Distributions (EVD) : the Gurnbel Type I, the Frechet Type I1 or the Type III distribution.

We used the Generalized Extreme Value (GEV) Distribution ( Maritz and Munro, 1967 ) to solve extreme values for small as well as large samples . A graphical plot was first conducted. Sextile estimates are evaluated and are used to derive the MLE of the parameters.

In this exercise we demonstrated the use of Extreme Value Theory to solve problems in three major areas : Environment ( Ozone Concentration ) , Meteorological ( Rainfall ) and Hydrology ( Flood ) We have identified the type of Extreme Value Distribution (EVD) the sampled data belongs to and return periods were also computed.

The main objective of this exercise is to use Extreme Value Theory to analyze a new area - a sporting event (the men's l00 m in the Olympics ). Chatterjee (1982) analyze and predicted the Olympic winning times but not without errors. Our analysis consist of two parts . First we analyze the data from 1900 to 1976. Our findings showed that the error percentage for the return periods of 1984, 1988, 1992, 1996 Olympics was less than 1%. Our results suggested that Extreme Value Theory could be used as an alternative method to analyze the 100 m event and hence a sporting event. Secondly we analyze the data from 1900 to 1996. Our findings showed that it belongs to the Type I11 EVD and the lower limit is 9.20s . We have also calculated the return periods for the 2016 and 2096 Olympics which is 9.83 and 9.70 respectively.Show more 126 15 - PublicationRestrictedCategories in algebra(1997)Sing, Siew Hoon
Show more Category theory provides a common framework for many branches of mathematics, especially topology and algebra. In this thesis, we mainly deal with those categories in algebra. Locally, the study of category theory helps in the understanding of the essence of important concepts in algebra such as injective mappings, subjective mappings, isomorphisms, identity elements and products, etc. Globally, it gives a way of comparing categories that used to be regarded as absolutely different things. The thesis yields a deeper understanding of the categories arising in algebra through the application of fundamental concepts in category theory, namely functors, natural transformations and adjoint functors.Show more 165 18 - PublicationRestrictedBlood lipids, lipoproteins, apoproteins and cardiovascular fitness in obese and non-obese Singaporean Chinese male adolescents 13 to 15 years of age(1997)Ng, Gillian Bee Kit
Show more Increasing affluence in Singapore during the last decade has led to a higher prevalence of coronary heart disease and obesity among Singaporeans. Recent evidence has suggested an unfavourable blood lipid / lipoprotein profile among Singaporean children and adolescents. Obesity and the physical fitness of Singaporean schoolchildren is of national concern. Very few studies, however, have examined the relationships between blood lipids / lipoproteins, obesity and cardiovascular fitness in Singaporean schoolchildren. Hence, the purpose of this study is to investigate these relationships in obese and non - obese Singaporean schoolchildren aged 13 to 15 years.

78 Chinese boys ( mean age = 13.52 + 0.6 SD ) were recruited for this study. AU subjects underwent 3 different tests : ( a ) body composition analysis - measurements of height and weight, 8 site skinfold thickness, and DEXA scanning to determine fat mass and lean body mass; ( b ) blood biochemistry analysis - drawing of 20ml of venous blood to analyse serum cholesterol, triglyceride, high density and low density lipoproteins, and apoproteins A1 and B ( c ) cardiovascular fitness testing - using the modified Balke protocol to determine 90zpeak of subjects.

Results showed that obese subjects had significantly higher levels of triglyceride and lower levels of VO2peak ( ml.kg-'min.' ) as compared to the non - obese subjects. A significant negative correlation also existed between VO2peak ( ml.kg-'.min-' ), triglyceride and obesity measures like BM1 and skinfold thickness. None of the other blood profile variables, however, had significant associations with obesity and cardiovascular fitness.

This study may be improved by examining the role of habitual physical activity on blood lipid I lipoprotein profile, obesity and cardiovascular fitness in Singaporean male adolescents.Show more 154 11 - PublicationRestrictedSome reactions of 8-aminoquinoline(1997)Thong, Kar Fong
Show more The reactions between 8-aminoquinoline and R2SnC12 (R - Ph, Me, n-Bu) have been carried out. 8-Aminoquinoline was found to form a stable 1:1 adduct, dichlorodiphenyl(8-aminoquinoline)tin(IV) (11a), with Ph2SnC12, as reported. With Me2SnC12:, it reacted to yield dichlorodimethyl(8-aminoquinoline)tin(lV) (11b), which was more stable in anhydrous benzene than in 'reagent-grade' CHC13. However, with n-Bu2SnC12, irrespective of the solvent used, 8-aminoquinoline was protonated at the p!ridyl nitrogen atom, leading to the formation of 8-aminoquirlolinium chioride (12).

(l11a) and (12) were prepared and characterized. They were required as the essential materials for studying the feasibility of the hydrolyzing reaction. UV spectroscopy was especially adopted to characterize the starting materials [ (11a) and (11b) ] and the decomposed products (12). The evidences gathered from a series of UV spectra indicated that these complexes, (11a) and (11b), would hydrolyze in the presence of water. This experimental result has an important implication in the mode of action for antitumour activity of diorganotin complexes.

In addition, (11b) which is s potential antitumour agent was successfully isolated. IR and NMR studies indicated the possession of a pair of cis chlorides and this was further confirmed by preliminary X-ray determination of the structure. This property is an important requirement for complexes to exhibit antitumour activity. The synthesis was further extended to the isolation of 8-amonioquinolinium dichloride (22) and 8-ammonioquinolinium diphenyltetrachlorostannate (23). These two new compounds were characterized spectroscopically. Hopefully, X-ray crystallography analysis can be carried out with the intention of determining the structural parameters important for antitumour activity.Show more 136 15 - PublicationRestrictedCounting models(1997)Cheong, Yin Ling
Show more This project is a study of beginning first-order model theory, up to a point sufficient for an exploration of Vaught's theorem: there is no complete first-order theory with exactly two nonisomorphic countable models. The exploration of this theorem requires, in the first place, the knowledge of the notions of a first-order language, a complete theory, models and isomorphism of models; next, the understanding of theorems such as Completeness Theorem, Compactness Theorem, Lowenheim-Skolem-Tarski Theorem and Omitting Types Theorem. Lastly, atomic models and saturated models are also given a close look at after which these results would enable us to discuss the theorem by Vaught.Show more 110 15 - PublicationRestrictedGeometry in "Jiuzhang Suanshu" and Liu's commentaries(1997)Phan, Wai Mun
Show more "The Nine Chapters on the Mathematical Art", (九章算术, Jiuzhang suanshu) is a compilation of works on mathematics from the Zhou, Qin to Han Dynasties (c 11th century BC - 200 AD). Presented in the format of problems, answers and algorithms (术, shu), the book contains 246 problems on mathematics, which were encountered in everyday life then. The mathematics involved range from arithmetic, algebra to geometry. Based on the nature of the mathematics involved, the works were sorted into nine chapters and compiled into a book, that is, "The Nine Chapters".

Through the decades, many mathematicians had written commentaries on the book. The more significant commentaries was that written by Liu Hui in 263 AD. Through his commentaries we were able to see more of the concepts behind the mathematics presented in "The Nine Chapters".

The focus of this academic exercise will be on the area of geometry reflected in Chapter 1, 4, 5 and 9 of "The Nine Chapters". Mensuration problems related to areas and volumes of various structures commonly seen in those days were discussed. Algorithms for the determination of sides of right-angled triangles and their applications were also included.

In the first part of this exercise a brief account on the background and contents of "The Nine Chapters" will be given. This is followed by discussions, on the geometric aspects of the book. Next, based on Liu Hui's commentaries, we will attempt to look into the principles that were possibly used to derive the algorithms for the mensuration problems presented. Finally, we shall look at Liu Hui's discoveries on some of the inaccuracies of the works.Show more 156 31 - PublicationRestrictedThe use of computer for timetable scheduling (a prototype)(1997)Tham, Thomas Kine Chuen
Show more Timetable scheduling has been a tedious and ongoing process done manually in NE. Clashes do occurred and changes need to be made even after the a schedule is supposedly planned. Certain days will not end before 8 p.m. for some staffs and students. For those who deal with timetable scheduling and thus perceive the complexity of the problem, these events are common and not alarming. In this academic exercise, a computer program based on Visual Basic 4.0 is written to provide an exploratory tool for timetable scheduling through the use of computer. Certain assumptions are made to reduced the complexity of the problem so that it is something manageable to start with. The main assumption made, is that the facility in NIE is unlimited, not only in quantity, but also in size. That is, there is always rooms when needed and the lecture hall can always accommodate the entire cohort.

The basic principle of the program is "mix and match" while manipulating with the constraints. The program enables the followings:

(a) Changing the number of time slots in a week.

(b) Forming tutorial groups automatically in two different methods.

(c) Randomizing the order of modules or pre-arranging them in a preferred order for insertion of timetable.

After studying the outputs churned out by the program under different combinations, it is clear that no BEST combination exists. The output varies with the number of students and the subject combination of the students. However, by inserting all the three-hour lessons first and the one-hour lessons last yields a better output than any other permutation. Also, by considering the modules with the largest combination of students first is least likely to have clashes.

Due to the short duration given to this academic exercise, the program is only customized to cater for BABSc (Yr I to IV), DipEd (Yr I & 1T) and PGDE (Pri & Sec). Also, all tutorial groups are fixed to have twenty-five (or less) students. While imposing these limitations, a reasonable scope of work is constructed. Nevertheless, further extension has always been the consideration when writing the program. Hence the program has created an opening for the use of computer for timetable scheduling.Show more 122 16