The purpose of my project was to prove if the seeds of invasive plants are spread throughout the Peace region in hay harvested by local farmers. Invasive plants are so dangerous because they adapt to their environment fast and some of them can cause harm to both animals and humans. Within a year they can completely wipe the ecosystem out of native plants. Many invasive plants are either poisonous or can affect the systems of the animals body’s. I collected 22 hay samples from local farms around the North Peace region. I conducted a survey to help collect information about the samples. A pretest was conducted to determine which of two homemade sifters (one with three layers of decreasing size wire mesh, and one with 6 layers of materials with larger size holes) was the best for sifting through hay. I was able to determine that the larger sifter was easier for sifting hay. I sifted through all 22 samples with the larger sifter. I individually looked through each layer and removed what I believed to be seeds. Each seed was individually bagged, labeled, and photographed through a microscope. After each seed was photographed they were planted to help identify the seeds. I contacted a seed specialist. I was able to send him the images of my seeds. He helped me to identify my findings. I removed a total of 5568 potential seeds in my 22 samples. Out of all the potential seeds found 628 seeds were invasive. All invasive plants identified either cause pain to animals or they easily over take the native plants.

本實驗主要闡明了三件事，1.如何去尋找在光學戲法上，其隱形區位置所在，並擺脫公式，從國中生就能懂得光學知識，來進行推論。2.解決仿照TheRochesterCloak不如預期的問題。3.捨棄TheRochesterCloak的作法，用我們自己的方法，打造一座隱形魚缸。 在1.這點上，當我們用平行於主軸的視線，平視透鏡時，物體若在接近焦點旁，其所成的像，會有部分落於，視野上的視覺不可見區域，以此為隱形理論基礎，透過不同透鏡組合及從視角、焦距、透視比例等方法，來達到使參考目標物所呈現的像，與原物為1:1比例且為正立，進而出現真正隱形效果。 最後，利用所有的推論和數據，我們使用自己的推算方式，來利用3D印表機，打造一台讓魚消失的隱形魚缸裝置。

Nowadays, the most of waste materials are incinerated and generated the toxic gases in 日本. On the other hand, the Hydrogen gas (H2) has attracted attention as clean energy due to no emissions of toxic gases. In this work, we investigated that the new hydrogen evolution system using waste materials, such as aluminum (Al) foil and lime desiccant, and also investigated their reaction mechanism. The grinded desiccant was added to Erlenmeyer flask containing 300 mL of water. After dissolution the desiccant, the Al foil was added to the solution to begin the reaction. Generated gas was determined by water displacement method. The gas components are identified by gas chromatography. We found that the waste material reaction combined with waste lime desiccant and Al foil could be used for one of the hydrogen evolution system. This reaction is depended on solubility of lime desiccant, thus mean solubility of CaO in water. The Al foil is reacted with the desiccant more than 20 times of reaction stoichiometry. The calcium ion or calcium complex ions are involved with the excess reaction of Al foil.

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.

本研究以蒙日定理「平面上三圓彼此的外公切線交點共線」及其對偶定理「平面上三圓彼此的內公切線交點與另一圓的圓心的連線共點」出發，探討三圓更多由內、外公切線所產生的共點共線性質，進而探討四圓以上的情形，以及正多邊形、圓錐曲線等位似圖形，並推廣至空間中的球體。正如本研究作品名稱，我們將鮮少人研究的蒙日定理萌發出新枝，在日夜中茁壯，甚至最後有驚人的發現「在空間中n個外離的球，任意1個球的球心與另n-1個球的蒙日點連線會共交一點，此點稱之為n球的蒙日點」，此「點」發現，讓人不禁對宇宙中星體之間的關係產生更多無限的想像。

本研究主要探討地震造成的纜車晃動，藉由自製的地震模擬器與纜車系統，探討各因素對纜車晃動之影響，設計纜車系統和車廂的減震裝置。研究結果顯示：一、地震時纜車斷電停駛位置愈靠近塔柱、相同長度纜繩上車廂個數較多、纜車重量較重、纜車臂較短，纜車晃動時間相對較短。二、所設計之減震裝置中，利用夾層中鋼珠轉動，使地震時只有外層纜車晃動而內層纜車輕微滑動的「雙層纜車」效果最佳。纜車系統塔柱則可參照建築物設置隔震元件，以減緩纜車晃動。本研究結果可望為未來應用之參考。

Detection of harmful chemicals used in industrial complexes is crucial in order to create a safer environment for the workers. Presently, most chemical detectors used in workplaces are expensive, inefficient, and cumbersome. In order to address these deficiencies, a novel sensor was fabricated to produce a unique spectroscopic fingerprint for various toxic chemicals. The sensor was fabricated by depositing several layers of silica spheres (diameter ~250 nm) on a glass substrate using evaporation-based self assembly. As the spheres assemble to form a photonic crystal, they also create void (i.e., air) spaces in between them. Once the spheres assemble as a photonic crystal, a spectrometer was used to monitor the reflectivity. The spectrum had a high reflectivity at a specific wavelength, which is governed by the average index of refraction between the spheres and the void spaces. As a foreign chemical infiltrates into the photonic crystal, it occupies the void space, which results in an increase of the average index of refraction of the structure. Consequently, the peak wavelength of the reflectivity spectrum red-shifts, which then confirms the presence of a foreign substance. While the as-grown photonic crystal is able to detect chemicals, it is unable to differentiate between chemicals that have similar indices of refraction, such as ethanol and methanol. In order to detect chemicals with similar indices of refraction, five pieces of a single photonic crystal (i.e. five pixel device) were exposed to different silanes, which changed the surface chemistry of the silica spheres in the photonic crystal. In turn, the five pixel device was able to produce a unique chemical fingerprint for several chemicals, which can be calibrated to detect toxins in the workplace.

In this project, we defined a mid-tangent point with respect to a fixed point X and a tangent at a point Y on a planar curve C as a point on the tangent that is equidistant from X and Y. We studied the locus of mid-tangent points of conic sections. We found that the locus of mid-tangent points of most conic sections are non-linear curves. However, we observed and proved by using Euclidean geometry that the locus of mid-tangent points of circles are straight lines. The mapping defined by mid-tangent points was studied further. The similarity between a mid-tangent mapping and a stereographic projection was displayed as a one – to – one correspondence function. We also extended the concept of mid-tangent points to three dimensional space and found that the similarity with the stereographic projection was retained in higher dimensions. Finally, we studied the locus of mid-tangent points of a sphere to create a mapping of the sphere to a plane.

利用化學合成法合成出聚苯胺及 MEH-PPV，經過一連串的製程作出高分子發光二極體（PLED），再用 I-V 儀量測。實驗中以聚苯胺及 MEH-PPV 的薄膜厚度為變因，進行實驗。 電壓值為 10V，量測樣品通路上的電流。一開始電壓在跑時，量到的電流都為 0A，所得到的圖形為一水平直線；當電壓到達一個值時會向上爬升，但爬到一個階段後圖形呈現鉛直掉落至電流為 0A，圖形又恢復成水平直線。過程中看到了薄膜厚度對樣品確實有影響，又鋁電極的厚度不能承受過大的電壓，所以，用銦粒壓在元件上藉以保護。 Using Chemiccal polymerize PANI and MEH-PPV make through a series Polymer light emitting diode（PLED）Produce.then using I-V meter surveies. PANI and MEH-PPV change of thick proces.Experiment design I-V volt for meter conduction of current of sample .The voltage moving.First meter current is obtaining the figure is horizontal when voltage increase to a special value , but increase a while , the current will fall down to zero volt. Figure will go to horizontal that sample will change .Thick is different,and aluminum cathode can not suffer too much voltage .otherwise will burn.

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.

我們在討論 John Mason 的 Thinking Mathematically 時，發現一個有趣的問題：「隨便寫下一個 0 和 l 的排列，若連續兩個相同的話， 在它們下面寫一個 0 ，否則寫一個 1 。重複這過程直到你只剩下一個阿拉伯數字數字。能預測最後一個是什麼嗎？」如： \r \r 此題看似簡單，但涉獵其中後，卻令我們沉迷於它的奧秘，進而想繼續探討。我們能預測最後一個數嗎？能擴展這個系統嗎？能知道 1 的個數嗎？

We all do it – walk along with a cup in hand, and carelessly spill it. While it’s usually more annoying than anything else, it happens to affect almost all of us, and little is done to minimise the likelihood of it occurring. So my aim was to explain the physics behind why we spill drinks when we walk, and to investigate how we can minimise the likelihood of this occurring. I broke this investigation into two distinct parts, explaining the system of the cup, and explaining the effect of walking. From initial observations, it was clear that the cup was a resonating system. Like any resonating system, the cup has a natural frequency. When the cup is oscillated – moved back and forth – at near this frequency, the size of the liquid oscillations is very large. This is because the acceleration is in phase with the motion of the liquid, so in each cycle maximum energy is input into the system. In my investigation I experimentally measured this natural frequency, and created a mathematical model to explain this frequency. It was also found that as the size of liquid oscillations in the cup increases, so does distortion of the fluid surface, possibly enabling spilling. To systematically analyse the effect of walking, I had subjects walk on a treadmill, so walking surface and speed were controlled. However, I also needed an accurate way of measuring the motion of a carried cup. Firstly, I tried to use video analysis; however I found this far too imprecise for measuring small changes in velocity of a cup. In the end I used a smartphone to record the acceleration of a carried cup, as acceleration is what causes the movement of liquid in a cup. This allowed surprisingly accurate measurements to be made, and allowed both the size and frequency of the acceleration to be recorded. In order to relate the system of the cup and the oscillation provided whilst walking I conducted a qualitative experiment into the effect of stride frequency on the likelihood of spilling. When stride frequency was very close to the natural frequency of the cup, spilling occurred almost instantly, while it did not occur if stride frequency was much higher or lower. In the end, my research showed that to minimise the likelihood of spilling your drink walk slowly, use a narrow cup, focus on walking smoothly, and fill the cup well below the rim. Despite this, some people happen to be much smoother cup carriers than others, likely due to their individual biomechanics. And, if you really don’t want to spill your drink, you can always use a lid.