Tradescantia (Tradescantia fluminensis) is the worst weed in New Zealand. By smothering and shading out seedlings, Tradescantia prevents forest regeneration. Current control methods are ineffective and simultaneously cause harm to native forest. In 2011 Neolema ogloblini, a Brazilian beetle was introduced into New Zealand as a biological control for Tradescantia. To be successful in New Zealand, a country with different environmental factors, the beetles’ ranges of preference (temperature and light intensity) had to be investigated. A gender specific trait also identified, to enable desired sex ratios within founding populations to be selected. [18] This would ensure that the beetles are not released in areas of physiological stress, and can be optimised to have the greatest impact on Tradscantia. To establish how the intensity of light affects the distribution and amount of Tradescantia eaten by N.ogloblini a choice chamber investigation was conducted. Different layers of shade cloth provided a range of light intensities 150-3450Lux (likely to be found under forest canopy where Tradescantia is problematic). Thirty beetles of a range of sizes and approximately same maturity were randomly distributed through the chambers. Each chamber contained a shoot of Tradescantia with 5 leaves. After a 24hour period the number of beetles in each chamber were counted and the amount of surface area of the leaves eaten measured. The effect of temperature on the amount of leaf surface area eaten was investigated by selecting 90 beetles of a range of sizes and withholding food for 24hours. Five beetles were placed in each of three containers containing two leaves. Each trial container was precooled/warmed to the test temperature before the beetles were added. Leaves of a similar size, shape, mass and maturity were used. All leaves were genetically identical and collected from the same location. Sets of three containers were held in the dark at the following temperatures for 24hours: 9°C, 15°C, 20°C, 25°C, 30°C and 35°C. The surface area of leaf eaten at each temperature (mm2) was calculated. Lastly, microscopic dissections were conducted, using 32 beetles ranging in size, to establish if length (measured from the top of the head to the base of the abdomen) could be used as a phenotypic marker to identify beetle gender. While only a very weak positive relationship between increasing light intensity and the number of beetles was found a significantly higher area of leaf was eaten at a light intensity of 3450Lux compared to 150Lux. The amount of leaf area eaten is significantly reduced at temperatures of 15˚C and below, and significantly increased at 35˚C. There is no significant difference in the amount of leaf area eaten when comparing temperatures between 20-30˚C. Females have on average a larger body length (median=4.92mm) than the males (median=4.215mm). Therefore, sites with warmer temperatures in dappled light conditions (3450Lux) should be prioritised for the release of N.ogloblini, as this is the location in New Zealand at which their use as a biological control will be optimised. Beetle length can be confidently used to select desired gender ratios.

本作品為環球數學城市競賽的考題之推廣（ International Mathematics Tournament of the Towns, Senior A-Level Paper, Fall 2009, No. 7 ），然而此題目本身比較接近Scientific American （ Feb 1979 ）中 Martin Gardner 的文章 The Rotating Table 所提出的問題。 而此問題的多邊形版已被數學家解決(Ted Lewis & Stephen Willard, 1980, The Rotating Table,Mathematics Magazine, 53,Page 174-175.)。然而此份作品採用簡潔的初等數學歸納法證明了原本的多邊形情形，且專注於探討條件改變為m=n-1時的多邊形情形。 m=n-1時的情形是前人所沒有做出結果的，且m=n-1的情形遠遠比m=n 的情況來得複雜多變，其中估計上下界所使用的許多組合技巧相當特別。然而其中當n為3 和5的倍數時有比較特殊的情況，這一個部分僅能給出目前得出的k值上界。而其他情況則能夠找出所有的k值。

本文籍由一套數學遊戲的必勝方法及其背後潛藏的數學原理，來作為研究目標。透過研究德國數學家E.Sperner 提出的方法所延伸的數學遊戲，來解決潘建強、邵慰慈兩位教授留下來沒有證完的遊戲結果[1]，並將遊戲增廣至三維空間的探討且得到如下的結論： 一、平面棋盤 (1)不可換色，先下者恆勝，其最快獲勝方法，為依所下位置的三角形衍生子圖周界走。 (2)可換色，獲勝規則由棋盤的總頂點數決定，若棋盤的總頂點數為奇數，先下者獲勝；若棋盤的總頂點數為偶數，則後下者獲勝。 二、空間棋盤 (3) 不可換色，先下者恆勝，而最佳下法，則是下在大四面體本身內部的某一點，且其最快獲勝方法為，依正四面體稜邊所下位置走。 This study is mainly about an invincible method of a mathematical game and its theory from which it is derived. We want to solve the problems left by Professor Poon, K.K and Professor Shiu，W.C. and meanwhile extend it into three dimensions through the method brought up by E. Sperner[1]. On two dimensional case, the first player will win the game forever on condition that these two players can't change their chesses colors at will. And the fastest way to win will be just putting the chesses that along the baby triangle boundaries. If both players can change their chesses colors randomly, count the chesses number before starting the game. It is calculated that if the number of the total chesses is odd, the first player will win the game in normal and logical circumstances. On the contrary, if the number of total chesses is even, the latter will win. On three dimensional case, the first player will definitely win the game without allowing changing chesses colors. And the best strategy is putting chesses in the inner of the big tetrahedron; what’s more, going along the edge of the tetrahedron will be shortest way to win the game.

本研究主要以一連串地震分析，來討論台灣地區地震能量釋放的型態。首先求出地震活動參數，接著再繪製地震規模的年發生率，最後推算台灣地區地震能量釋放時前餘震與主震所占之比重。在地震參數上，發現地震活動度較高的月份中，在該月都發生了芮氏規模六級以上的大地震，因其餘震發生的頻率較小震頻繁，因此造成其a 值較大。另外本研究發現，在大地震來臨之前，地震A 值會升高，應可視為其A 值升高之因是由於前震的關係。在地震規模年發生率方面，繪製出圖表，最後發現台灣地區地震仍以小震多，另外大地震則有一定週期。在研究最後，了解台灣地區地震常數之後，本研究更以ESRI 的GIS 軟體ArcView9.0 版輸出台灣地震目錄，並從中了解台灣的震測儀器發展。This research presents a series of earthquake analyses to discuss earthquake’s energy release type. First, we evaluated earthquake’s constant and charted the percentage of earthquake measurement every year. Finally, count the after-shocks and the major earthquake measuring 6.0 and above on the ML happening in Taiwan area. Because the after-shock frequency is more than light earthquakes, as a result it causes the“a” enumeration is large. According to the percentage of earthquake measurement happening frequency every year, we illustrate a chart. Finally we find that in Taiwan area mirror earth-quakes account for a large percentage and major earthquakes happened regularly. When we realize the constant of earthquake, the study folds a variety of layers by using ArcView 9.0 edition of GIS (Geography Information System) of ESRI , knowing the earthquake in Taiwan.

My project is a robot designed to clean windows and eliminate the need for human labor. My ultimate aim for this project is to develop my robot to clean high-rise buildings as well as homes. The current version of my robot is designed to clean only house windows. The idea to invent a robot that would automatically clean windows came to me when I arrived home from school one day and found my father struggling to clean the outside of our living room windows because he suffers from back and knee pain. During my research I stumbled upon high-rise window cleaning accidents in which people have lost their lives and this gave my project greater purpose. The major challenge I faced when designing my robot was getting my robot to stick to a vertical window while maneuvering around its surface without falling off. My solution was to use vacuum technologies, suction cups and direct current motors in my design. My robot is made up of a mechanical system, an electronic system and a pneumatic system. The mechanical system consists of direct current motors that drive the two arms of the robot backward and forward through a rack and pinion enabling movement. The pneumatic system provides the vacuum that enables my robot to stick to the window and also consists of pistons that lower the suction cups onto the glass. The electronics system is made up of a microcontroller that uses transistors to control the robots various components. Some key features of my robot include the new split unit design which includes a cleaning unit and a control panel that allows for a decrease in the weight of the device, ultrasonic distance sensors for window edge detection and a self drawing cleaning progress map which the robot displays on the LCD screen on the control panel. Gauges have been added to monitor pressure and vacuum levels in the system so that the user is aware if a problem were to occur. The dual squeegee design includes a squeegee on either end of the horizontal arm which are raised and lowered at certain times while the robot maneuvers across the window to result in the most effective clean. Attached to the squeegees are microfiber cleaning pads that are used to clean the window. I plan to one day develop my robot to clean high-rise buildings so it minimizes the risk of workers losing their lives.

This project aims to create the polar equations from the relation of the points on the centre line of the water twisted from Butterfly sprinkler heads. The water path includes inner rim, outer rim and centre line laying in the middle of the water path is used Rhombus’s property. The diagonals are perpendicular bisectors of each other to create the centre line. Then we create the polar equation of the centre line of water that twists from 4 types of the Butterfly sprinkler heads: edge frame, curve frame, STL and STL rotary. The polar equation of outer rim and inner rim is created by adding and removing the “ f ” value ( ; is the distance between the outer rim and the centre line, and is the geometric sequence that is ) of the coefficient (a) of the polar equation respectively. The results show that the formal equation of the centre line is which can explain the different properties of Butterfly sprinkler heads. If “ f ” value is increasing the water path and the blade will be wider that affects droplets distributing thoroughtly. Furthermore the relationship between the volume of water and the radius of water distribution can be processed to find the least time that can increase the appropriate moisture level of soil.

在物理馬戲團這本書中提到：「當你泡即溶咖啡或攪拌奶精的時候，用湯匙輕敲杯壁看看，添加奶精後攪拌時，敲擊的聲音與添加前明顯不同，為什麼？」這本書的解答是：「當粉末溶解的時候，藏在粉末裡的空氣就會跑出來。因為空氣裡的音速低於水裡的音速，在空氣與水混合的環境裡，音速也比在水裡低。當水裡不斷有空氣混進去時，這個容器的共振頻率和它裡面的音速有關，所以也會降低。因此你會聽到較低的音調，直到空氣全部跑光。」我們利用指向性麥克風以電腦錄音後以Adobe Audition 軟體分析聲波頻率，覺得這個說法有點問題。例鹽水溶液音速較水高，敲擊時的音調卻較水低。由敲擊一黏於裝水水盆中之空杯，與敲擊杯內裝同一水位之水之杯子，頻率非常接近。告訴我們影響頻率的是靠近杯壁一層有效質量。因鹽水溶液密度較高有效質量較大，所以頻率較低。以密度的觀念檢視裝有溶液之杯子被敲後的頻率是對的。但對杯中有懸浮物就不然，例如流體中含有氣泡，則混合體之密度必定變低，有效質量變小頻率應變高。但實驗發現含有氣泡時頻率是變低的。可見氣泡還有其他的影響力高於密度對音調的影響。 流體的振動應是會壓縮到氣泡，氣泡與流體間之力學交互作用為何會使頻率下降，正是我們要找出的。 The Flying Circus of Physics has a question “As you stir instant cream or instant coffee into a cup of water, tap the side with your spoon. The pitch of the tapping changes radically as the powder is added and during the stirring. Why?” The answer is, “The air trapped in the powder is released as the powder dissolves. Since the speed of sound is lower in air than that in water, the speed of sound in the air-water mixture is lower than that in pure water. During that period while the air escapes the container, the resonant frequencies of the water, which depend directly on the speed of sound, will also be lower. Hence, you hear a lower tone until the air escapes. “We then tap the coffee cup and generate an audible tone. The signal picked up by the microphone . The same signal is also studied using Adobe Audition, a waveform processing and analyzing software. We find the assumption is wrong, the speed of sound is higher in sugar solution than that in water, but we hear a lower tone. An effective layer of fluid adjacent to the glass wall is set into motion when we gently rub the rim of the wineglass. The thickness is about the same whether the fluid is inside or outside the glass. This explains why the frequency drops when the liquid is added to the system. When the density of the sugar solution is higher, the mass of the effective layer is higher. But what the presence of the bubbles and the theoretical explanations must NOT rely on are: Use effective density argument: One should not just use a change in the main density to try to explain why the frequency is lower. I would think that the bubbles are compressed a little bit by the vibrational motion of the glass communicated to them through the fluid. But how do the bubbles interact with the fluid under this setting? This is what we need to work out.

The continued growth of dairy farming in NZ and the move toward keeping cows on stand-off pads has seen a major increase in two significant waste streams, the wood fibre that is scrapped off the surface of the standing pads and the effluent that is now concentrated at the site of these pads. In combination these waste streams offer the farmer an opportunity to recycle valuable nutrients back into the soil as an up-valued soil conditioner. This investigation explores vermicomposting as a tool to efficiently manage these two significant waste streams. Sludge was removed from a settling pond and mixed with a range of carbon products that are recommended by Dairy NZ for use in stand-off pads: wood chips, post peeling, sawdust and also wood shavings (used in calf sheds). The wood fibre/sludge mixtures were assessed on their acceptability to tiger worms (Eisenia fetida) by measuring the pH of the mixture and seeing if they corresponded with the preferred pH for tiger worms. The vertical spatial distribution of tiger worms was measured over a period of 15 days and the rate at which the worms moved into the different mixtures was assessed. The worm mass before and after this 15 day period was also measured to ascertain the mixtures’ ability to support worm growth. Finally, different ratios of sludge and post peelings removed from a calf shed were used in a choice chamber experiment to establish the worms’ preference. Tiger worms were used throughout the investigation as they represent the worm species most widely used in vermicomposting in New Zealand. Tiger worms feed on decomposing organic matter, bacteria and fungi in the upper organic horizon of soil. All of the unused wood fibre and dairy sludge tested lay within the acceptable pH range for tiger worms. Wood fibre exposed to large amounts of urine ie calf shed post peelings, that lie outside the acceptable range can be favourably adjusted with the addition of dairy sludge. All the particle sizes of the wood fibre tested were found to be acceptable to tiger worms and capable of supporting increase in their body mass beyond that of the compost. Due to the observation that the worms did not integrate themselves as fully in sawdust as the other fibres tested it is recommended that further investigation should be carried out before sawdust is used for vermicomposting. While a comparison of the average worm density in each mixture may indicate a preference for post peelings this cannot be statistically proven and more trials are recommended. The preferred ratio within the limits that were tested is 1:3 calf shed post peelings to sludge (41% dry weight). Vermicomposting can therefore be recommended as a possible onsite technology to process the twin waste streams of wood fibre and effluent generated by dairy farms. The next step would be to implement medium scale field trials with a continuous windrow system, testing resulting compost for its nutrient content and then comparing this output to that of current practises

Diarrhoea is an infectious disease that claims many lives (particularly among infants) and is known among many other infectious diseases, to have a relationship with climate. This projects quantifies this relationship by comparing health insurance treatment claims for diarrhoea and anti-diarrheal drug sales data from the private health sector with temperature and rainfall data provided by the South African Weather Service. The data were then analysed and show that incidence is highly seasonal and varies among regions with different seasonal climates. The results show that climate variability can explain 73% of diarrhea incidence variation with rainfall explaining 8% and minimum temperature explain the other 65 %. Preliminary predictions of future monthly percentage increases in incidence were then made for a series of time ranges. This project demonstrates that with predicted climate data one can predict future variations of diarrhoea allowing the health sector to be adequately prepared.

My purpose of the Research was build a small, compact device for the GoPro, which minimizes shocks that are typically caused by running and makes the video stable. The device must fit into a backpack and must be designed for the GoPro. This scenario raised two central questions for me: Which laws of physics are used for the stabilization of the camera? How can those laws of physics constructively be transformed into a working device? I have built four prototypes. To know which prototype was the best, I compared them and gained data into diagrams. The result with the last prototype was very impressive and encouraging, whether your are walking, running or skiing, the videos were no longer shaky. My final prototype consisted of a hollow tube which extended vertically. My conclusions: First the handheld camera mount mustn't be too light, as the inertia of the device is too low. Second it mustn't be too heavy, because you normally have to hold it over a certain time interval. Inertia as well as lever principal were essential to produce a smooth video. The most difficult part to build was the fully gimbaled suspension because it requires as little friction as possible and it must be precise and solid.

Figs have become an expanding industry here in New Zealand and are a current export fruit which could potentially provide a large amount of profit to both growers and the New Zealand market as a whole. Nicola’s family has about 10 acres of fig trees. They sell the figs locally and as an export. They generally sell for about $13 per kilogram here in New Zealand and $26 in the USA. However, figs only have a shelf life of about 7 days. This is because at present there is no proven pre or post-harvest treatment or method of storage that helps to decrease the rate of decay of the fig fruit. After researching post-harvest treatments for figs, Nicola found a report which claimed to have developed treatments that increased the shelf life of figs by about 5 weeks. With this kind of increase, it would be possible to transport, store and export figs over longer periods of time without running the risk of losing large amounts of produce, or delivering unsatisfactory fruit to customers. Nicola developed 7 different post-harvest treatments based on the ones that had shown promise in earlier research. These were hot-water baths of different temperatures, both with and without different bleach concentrations. To test these on the fruit she set up four experiments – a dry matter test, a firmness test (using a penetrometer), a colour test and observation of detrimental features of the fig. She tested these treatments at 0, 7, 14, 21 and 28 days from harvest. Nicola found that after 7 days, the firmness of all of the figs that had been treated had decreased to a large degree. The only figs that did not have a massive decrease were the untreated fruit. However after about 14 days, the firmness of all of the fruit became about the same and after this 14 day mark, she would not have considered any of the figs to be edible. However, in the appearance tests, it seemed that the treated figs that had the least amount of mould and rot were the ones that had been treated with higher levels of bleach such as the 55 degree Celsius water bath with 0.003L of bleach to every litre of water, and the 35 degree Celsius water bath with the same concentration of bleach. Overall, Nicola’s results showed that the hot water bath, and hot water bath and bleach post-harvest treatments did not slow the decay of the fruit in the earlier weeks after picking. In effect, Nicola’s research showed that the information she had relied on to help plan her study had claimed too much and that the treatments were less effective than had been stated. More research will be needed to find a more reliable way to improve the shelf life of figs.

The objective of the project is to develop a novel biomimetic membrane and/or a scaffold for the said membrane. The approach of the project is to use animal skin from the domesticated pig or fish as a scaffold material for the adherence and growth of human skin fibroblasts to create a biomimetic membrane that can be used in medical applications as an alternative to today’s gold standards of Xenograft, Allograft and Autograft procedures. The biomimetic skin membrane can be used to treat victims of burns or scarring with a natural material that would be eliminated via natural bodily functions while eliminating the side effects and drawbacks such as scarring, secondary infections and tissue damage resulting from the current gold standard graft procedures on donor sites. Pig and fish skins were treated with ethanol and dehydrated followed by perfusion with Phosphate buffer solution and Cell culture media. Human skin fibroblasts (NF3 cells) were seeded on the animal skin scaffold. The human skin fibroblasts were then observed to determine their morphology and membrane formation properties. It was observed that the human skin fibroblasts were able to adhere to the non-human skin scaffolding and proliferate. More research is needed to determine their viability as a biomimetic membrane.