全國中小學科展

四等獎

簡易方法測量電遷移率

氯化鈉水溶液滴上染料,外加互相垂直的電場和磁場後,離子受到和電流方向垂直的勞侖茲力而移動,因黏滯力作用而形成漩渦偶極子;由漩渦偶極子的位置隨時間變化,可得到漩渦偶極子的運動動量通量,進而算出鈉離子和氯離子的電遷移率和(μ++μ-)。 用氫氧化鈉水溶液實驗時,因正離子的電遷移率小於負離子,漩渦偶極子一面移動一面偏轉,由移動的位置隨時間的變化可求得鈉離子和氫氧離子的電遷移率和(μ++μ-); 由偏轉量可求得兩種離子的電遷移率差(μ--μ+)。用氯化氫水溶液實驗時,漩渦偶極子偏轉方向和前者相反,由偏轉量可求得兩種離子的電遷移率差(μ+-μ-)。 霍爾效應實驗可求得離子的電遷移率差,用氯化鈉、氫氧化鈉、氯化氫、氮氣奈米氣泡、和氧氣奈米氣泡水溶液作實驗,和漩渦偶極子法對照比較。

Enhancement of Online Stochastic Gradient Descent using Backward Queried Images

Stochastic gradient descent (SGD) is one of the preferred online optimization algorithms. However, one of its major drawbacks is its predisposition to forgetting previous data when optimizing through a data stream, also known as catastrophic interference. In this project, we attempt to mitigate this drawback by proposing a new low-cost approach which incorporates backward queried images with SGD during online training. Under this new approach, we propose that for every new training sample through the data stream, the neural network is optimized using the corresponding backward queried image from the initial dataset. After compiling the accuracy of the proposed method and SGD under a data-stream of 50,000 training cases with 10,000 test cases and comparing our algorithm to SGD, we see substantial improvements in the performance of the neural network with two different MNIST datasets (Fashion and Kuzushiji), classifying the MNIST datasets at a high accuracy for the mean, minimum, lower quartile, median, and upper quartile, while maintaining lower standard deviation in performance, demonstrating that our proposed algorithm can be a potential alternative to online SGD.

建構三種以上相異整數邊長的圓內接多邊形

前作「建構邊長為整數的圓內接多邊形」[2]中,我建構了多類兩種相異整數邊長的圓內接多邊形的一般式。本研究利用n倍角公式,建構三種以上相異整數邊長且外接圓半徑與所有對角線長均為整數的圓內接多邊形。 我依正整數的分割數將圓內接多邊形分類。除了正多邊形之外,6類圓內接五邊形、10類圓內接六邊形、14類圓內接七邊形。取畢氏三元數做變數變換,做出所有類型相異且有不同邊長的圓內接多邊形。另外在建構圓內接八邊形、九邊形與十邊形時,我考慮建構邊長相異且其中一邊為外接圓直徑的圓內接四邊形、圓內接五邊形與圓內接六邊形...等,將上述圖形做適當的伸縮與組合,即可以建構邊長皆為相異的整數的圓內接n邊形。研究過程也發現可用同一組一般式可建構不同的圓內接多邊形。最後推得各類非等邊長且外接圓半徑亦為整數的圓內接多邊形皆可尺規作圖。

The Waves Fish Controller

Our oceans, coasts, and estuaries are home to diverse living things. These organisms take many forms, from the tiniest single-celled plankton to the largest animal on Earth, the blue whale. Understanding the life cycles, habits, habitats, and inter-relationships of marine life contributes to our understanding of the planet as a whole. Human influence and reliance on these species, as well as changing environmental conditions, will determine the future health of these marine inhabitants Humans influence the whole environment even if they don’t notice , the growth of men and our increasing reproduction over the years results to an over consumption of nutritious products , which makes us exploit the wildlife more and more and in the same time take parts of its habitats for us to life in and throwing our non-needed materials in what’s left of the world. And that’s a big problem because the Eco-System was just fine before we started over exploiting it in a greedy and unreasonable manner, and since the ecosystem’s parts are related altogether in an ongoing circle , the absence or the destruction of one part of It may lead to the unbalance and even destruction of the whole organized system. And that’s why as humans, it is our first duty to take care of nature generally and both fauna and flora specifically, not because of a moral code of some kind; but to protect Humanity from ourselves, and to preserve the human kind from destruction and extinction. And that’s the main goal of our project, that’s to help us organize our fishing exploitative activities with how much can the environment handle from it.

利用水稻Near Isogenic Line篩選調控磷酸吸收相關之基因

因應人口增加,提升作物產量同時維持農業永續經營成為全球發展的重要課題,其中如何減少肥料使用以降低對環境衝擊為一重要關鍵;磷肥為作物生長必要元素,過度使用不僅加速礦產資源耗竭且造成環境汙染,若能提高作物磷吸收效率將可望減輕上述問題。水稻為世界三大主食之一,本實驗目的在於了解水稻吸收磷的調控機制,作為未來孕育高吸收效率水稻的基礎。選用稉稻(台農67號)及秈稻(台中在來1號)來檢測長期缺磷後再回復磷供給的狀況下這二個品種的生長狀況及地上部磷累積情形,結果顯示台中在來1號的根明顯較短,而台農67號第二葉磷酸累積較高,接著利用兩品種雜交所得之190個Near Isogenic Line進一步篩選磷酸吸收效率表現良好之品系,於養分充足下培養,或及在長期低磷培養後回復供給4天,比較各品系株高及幼葉和老葉磷酸累積量,未來將利用已知的基因多型性圖譜剖析造成差異之基因座,以了解水稻調控磷酸吸收的分子機制。

四角垛彩球遊戲研究

四角垛是「底層是邊長為n顆球的正方形,其上層在每顆球的中間排成邊長為n顆球的正方形,依此方式堆疊至最上層是邊長為n顆的正方形」。 本文主要探討的問題為:當四角垛最底層彩球用紅藍綠三種彩球擺定,上層每顆球的顏色由其下層所接觸的四顆彩球依照給定之規則來決定其顏色(紅或藍或綠),那四角垛最頂層那顆球的顏色為何?我們透過數學建模將此問題轉換為 的矩陣問題來解決,並得到如何最快求得答案的方法。另外,透過矩陣的可逆性與否我們可以判斷當給定四角垛哪些位置彩球的顏色後,即可推得四角垛中每顆彩球的顏色。

以直向、橫向、斜向磁磚鋪滿mxn矩形的研究

我們的主題是研究使用直向、橫向與斜向磁磚不交疊地鋪滿m × n的長方形的方法總數。磁磚總共有如圖A中間所列出的四種(其中著上藍色和綠色兩者統稱為「斜向的」磁磚),並且斜向磁磚不能夠有圖所顯示的交疊的情形。在1961 年的論文中給出了只使用直向、橫向磁磚鋪滿2m × 2n 的長方形的方法數的一個漂亮的公式,而2001 年的論文以一個較簡單的方法證明了這個結果。(1)(2)(3) 而我們先從固定 m 尋找遞迴式的方法出發,接著用m 的結果推出m + 1,最後期望能找出與論文一樣的一個漂亮的一般通式。

Territorial behaviour of the Eurasian Wren (Troglodytes troglodytes) during autumn migration and wintering in the urban environment of Hradec Králové, Czech Republic

In the present paper I studied the winter territories of the Eurasian Wren (Troglodytes troglodytes) in the urban environment of the city of Hradec Králové. The males of this species were detected through the aggressive reactions to the playback of its conspecific call. The Eurasian Wren territories were detected at seven out of the ten observation points in the city. The frequency of the territories decreased during the observation period from October to January and it was also affected by the structure of the biotope. It seemed that the wrens preferred trees and avoided lawns and isolated growths. That illustrates how important it is to maintain wildlife corridors in the cities. Individuals of seven other bird species were seen reacting to the playback of Eurasian Wren songs or warning calls. Eurasian Wren may be applied as an indicator species of the ecological value of the urban environment. Through this species, we can access such quality also for the human inhabitants.

利用VAE-pix2pix生成擬真的山脈模型

本研究利用NASA的SRTM 1 Arc-Second資料集來收集全球各地的地形高度圖(heightmap),也利用MapTiler網站收集相對應的衛星空照圖,用這些收集的圖像,訓練我們建構的VAE-pix2pix模型。VAE-pix2pix為Variational Autoencoder (VAE)及pix2pix (為一個Conditional Generative Adversarial Network)結合的模型,能將人工繪製的高度圖加上真實山脈應有的細節(包含尖銳的山脊、山壁上的紋路、連續的河流網路等……),並生成出相對應的擬真衛星空照圖。相較於原pix2pix模型,VAE-pix2pix所生成的高度圖及衛星空照圖會更接近於真實世界的地形高度圖及衛星空照圖,同時VAE-pix2pix模型也能透過改變latent code的數值來生成出不同風格的高度圖及空照圖,如地貌的顏色或雪線的高度等,這些都增加模型生成圖像的多樣性。為了使我們建構的模型能更廣泛的被應用,我們在Unity上開發了Unity客戶端,其生成的mesh可以讓使用者直接應用於遊戲的場景,簡化了遊戲中生成擬真山脈模型的任務。

以農業廢棄物芝麻稈做為紡織業常用染劑吸附材質之探討

本研究的重點是使用芝麻稈作為高效的吸附材,進而從水溶液中去除在染紡工業上常用的亞甲藍、剛果紅及雅里西安藍。在研究中,我們分別以吸附時間、pH值、吸附起始濃度作為操作變因,研究其物理、化學參數如吸附率、移除量、反應級數、吸附模式等等之變化[1][5]。使用UV-Vis光譜儀製作檢量線,推算各條件下所得之剩餘濃度,並由此計算其他所需之參數。本研究使用pseudo-first-order及pseudo-second-order進行動力學之分析,我們可以發現芝麻稈對於亞甲藍[3][4][5]、剛果紅[2]及雅里西安藍之吸附均符合pseudo-second-order模型;最佳吸附pH分析則可得知,亞甲藍於pH=5、剛果紅於pH=7,雅里西安藍於pH=8下可得最佳吸附效果;如使用恆溫吸附模型分析其吸附行為,則由實驗結果我們可以得知:亞甲藍符合Langmuir Isotherm及Freundlich Isotherm、剛果紅符合Langmuir Isotherm、雅里西安藍則符合Freundlich Isotherm;而其最大吸附量分別高達每克吸附材可吸附6624.75毫克亞甲藍、10815.74毫克剛果紅或18574.4毫克雅里西安藍。