三等獎

本研究旨在研究費馬多邊形數定理(任意非負整數必可表成k個k邊形數的和)的一般化情況，也就是說，任意非負整數是否能表成給定的二次多項式數列中所選取的γ項和。以數學模型敘述，就是探討對一個已知的二次多項式an2+bn+c，是否可找到一正整數γ，滿足∀x∈N∪{0},∃α1,α2,…αγ,使得x=∑γi=1(aαi2+bαi+c)。 本作品主要探討若此探究模型存在，那麼數列〈an 〉的一般式an2+bn+c與γ值之間會存在什麼關係，並期望能運用一個簡潔明瞭又一般化的數學式表示。本文亦提供另一個數學模型，探討γ值與某些特殊係數a,b,c之間的關聯性。而本文探尋[a/2]n2+[b/2]n+1,a∈N,b∈Z,a+b≡0(mod 2)(此為本文主要探討的二次式)，求得此二次式所對應之γ值的方法為先令p=[2a/(a+b)]+2，再藉由所建立的模型二，求出[(p-2)/2] n2+[(4-p)/2] n的γ值，接著再用所建立的模型一來求得[a/2]n2+[b/2]n+1的γ值，進而依循此方法最後得出任意形如[a/2]n2+[b/2]n+1的二次式之γ值。

EmerApp+ is software designed for intelligent devices as a personal security database manager. In case of emergencies, it is an application which integrates location, tracking, and communication tools. It is triangulated between a database to a communication server as well as a second which is NASA server that offers climate and seismic information for Mexico. This application has two sources of communication, SMS messages and a newly created social network. In case of natural disasters, an extension for drones has been developed for this application, enabling rescue teams to delimit the land boundary where the disaster struck. In order to speed up the search and rescue operations a triangulation of network-drone- smartphone is completed.

We present a study using microlensing event data from the Optical Gravitational Lensing Experiment (OGLE), recorded in the period 2002-2016 from the Galactic bulge. Our two algorithms are based on the standard point-source-point-lens (PSPL) model, and on the less conventional parallax model respectively. The optimal fit was found for each sample event in the chi-square optimization algorithm, along with the best fit parameters. Out of the 7 best fits, 4 show strong parallax effect. The microlensing fit parameters were then cross-matched with proper motion data from the Naval Observatory Merged Astrometric Dataset (NOMAD), to obtain lens mass estimation for four events. These were estimated to 0.447 solar masses, 0.269 solar masses, 0.269 solar masses and 17.075 solar masses respectively. All masses were within the microlensing mass interval for lenses found in similar studies. In this study, we conclude that the parallax model often better describe long events and demonstrate the importance of utilizing both PSPL fits and parallax fits, instead of only the PSPL model. By varying only 2 of the 7 parallax microlensing parameters instead of all simultaneously, we obtain plausible values for lens direction and lens transverse velocity: a method to investigate microlensing lens properties with no regard to its luminosity. In addition, we also present spectral classes of the NOMAD objects associated with each event, which is vital for future investigations to further confirm mass estimations. We present strategies to further enhance the algorithm to analyze the microlensing event light curve to better find deviations. We also conclude that our double model can potentially unveil the presence of dim lens objects (MACHOs) such as brown dwarfs, exoplanets or black holes.

Current medical intervention in cancer therapeutic methods has shown risks and side effects with normal tissues. This includes incomplete cancer eradication. In reference to numerous studies and literature reviews, a stimuli-responsive drug delivery system is selected as an innovative, safe and more assured treatment due to its site-specific release ability. This allows specific intervention upon the given stimulus which response to the presenting disease symptoms. Hence, we designed a ROS(Reactive Oxygen Species)-responsive BA-ADA(4-Hydroxyphenylboronic acid pinacol ester and 1-Adamantanecarboxylic acid bonded molecule) nanoparticle delivery system. In our study, ROS-responsive nanoparticle was designed and prepared based on a synthetic molecule from BA and ADA. A therapeutic payload, Doxorubicin, can be loaded into the nanoparticles and it can be selectively released within cancerous tissues whereby ROS level is over-expressed. This will enhance both therapeutic efficiency and reduce side effects. The stability and ROS-responsiveness of the particle were proven in a series of evidence-based experiments. The results showed a significant difference in cell viability during the experiments with healthy and cancerous cell samples. Further research will be required to extend the experiment in vivo.

乳癌是台灣女性死因第四名，其中的三陰性乳癌因具備高轉移力，又缺乏特定受體而不適用於標靶藥物治療或賀爾蒙治療法，所以其治療方法有其困難度。CID384634為2-phenynaphthyridone（2-PN）的衍生物，此藥物可藉由干擾微管蛋白聚合抑制致瘤性高的細胞株生長，於是我們想探討CID384634對於高度轉移性的三陰性乳癌是否也有同樣的治療效果。本研究以MTT assay和西方墨點法探討其治療效果與作用途徑，並發現CID384634可藉由回復雌激素受體表現，並且在合併臨床賀爾蒙治療用藥tamoxifen有明顯抑制三陰性乳癌細胞存活率。實驗也證實CID384634具有抑制上皮細胞及間質細胞轉換的作用。我們希望在不久的將來CID384634可以用來治療三陰性乳癌。

銦之化合物常被應用於半導體產業當中，隨著使用量的增加也提高銦污染流佈於環境的風險，若此污染物流布至土壤並累積於植物體內，則可能通過食物鏈而影響人體的健康。現今國內外鮮少有銦對植物影響的相關研究，因此本研究以培養基試驗，探討銦對模式植物阿拉伯芥生長之影響。結果顯示，當銦處理濃度為500 µM時，其生質量以及根長會受到抑制。MDA含量的增加，顯示銦會對阿拉伯芥造成氧化逆境，而穀胱甘肽與金屬螯合素並非阿拉伯芥在銦逆境下主要的抗氧化機制。本研究亦發現銦處理下會影響對錳、鉀、鈉、磷、鐵、錳、銅以及鋅的吸收。此外，X光吸收光譜分析顯示根部以及地上部中銦物種有明顯組成上的差異。於根部有42.9%的銦是以吸附於細胞壁的形式存在，這可視為植物對重金屬所採取「隔離」策略的防禦方式之一。

平原菟絲子對於多數植物皆會寄生，實驗中發現不易寄生於空心菜、地瓜葉、朝天椒，可證明具有寄生的選擇性。為了抑制種子的發芽，實驗無意間發現密閉中麵團黴可以完全覆蓋種子，但木瓜黴、柳丁黴、麵包黴卻沒有這種現象。麵團為穀類製品，易受黃麴毒素汙染，花生更易受黃麴毒素汙染，故選擇花生再次實驗，發現花生也能有效抑制發芽的效果。 103年5月觀察世博館旁與南寮漁港的菟絲子生長情形，從夏天到冬天都有菟絲子生長，104年8月經歷蘇迪勒Soudelor颱風和10月杜鵑Dujuan颱風過後，實地觀察發現，南寮漁港堤防外整片菟絲子全部消失，堤防內的依然存在。根據文獻顯示海水中含有35‰的氯化鈉，設計實驗發現泡過15‰以上的食鹽水後菟絲子就不會再發芽，另外，我們運用海水成分第二高的氯化鎂進行實驗，亦有抑制種子發芽的效果。

以製作適合高中生的英文篇章難易度自動分級為初衷，本研究採高中英文課文為語料，針對「如何分級」，意即從文章萃取哪些特徵、利用何工具或語料協助萃取特徵、以何工具分級等因素，進行研究與實驗，並建立一套新方法。首先進行前處理，再嘗試以單字、句型的數量或比例、句長、音節長、整合以上分析等各式特徵，支持向量機(Support Vector Machines)、隨機森林分類器(Random Forest Classifier)、決策樹分類器(Decision Tree Classifier)、卷積神經網路句分類器(Convolutional Neural Networks for Sentence Classification)等工具，進行將篇章分為高中一、二、三年級等三個難易度等級的測試，建立自動分級模型。最後製作成可供大眾使用的自動分級網頁。各項測試之中，最佳分類效能為整合各項特徵時得到的分類正確率65.04%，經模擬得知，此效能較過去研究，已有所提升。

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.

Parameters of traffic, road availability, and fare were integrated into a web-based application for determining the best public transport routes within Metro Manila in order to assist commuters in their travel planning, whether for business or for pleasure. A user-friendly interface was developed to obtain a user’s place of origin and destination, as well as preferences in travel time, mode of transportation, and cost of journey. By accessing the traffic roadway network of the metropolis, a real-time situation of road availability was obtained, and used in a modified Dijkstra’s shortest-path algorithm to produce a model of a real-time adaptive transport network of Metro Manila. From the model, an optimal route that considers the user’s preferences can be determined. This project will be immensely useful in helping both businessmen and tourists in planning their routes that will save on time and money.