全國中小學科展

四等獎

棋盤中矩形周長和最小的分割策略

題目緣由是數學奧林匹亞預選題的其中一題組合問題,題目探討在2^m×2^m的棋盤中(m∈N)先分割出對角線上的2^m一單位正方形,之後將剩下兩塊狀似等腰直角三角形的棋盤分割為若干個不重疊的矩形,求此棋盤被分割出的所有矩形周長和最小值。本文將原命題推廣至nn×n棋盤與m×n棋盤的情況,在2^m×2^m中達到周長最小值的矩形分割方式十分直觀,但證明過程中直接構造函數2x〖log〗_2 x以及利用琴生不等式等方法不甚直觀,於是我們在n×n部分的最後給出了另解,並說明原題為其特殊情況。 n×n的部分沿用原題之方法定義了十字分割,我們證明了利用完全十字分割可達到最小值,為4n(m+3)-2^(m+3) (其中2^m≤n

不同氮源的氮氧化鈦可見光光觸媒之製備與性質探討

本研究擬利用液態合成法,以尿素(urea)、硫脲(thiourea)與氨作為摻雜物與市售之TiO2粉末均勻混合,製備高活性於可見光下應答之氮掺雜的二氧化鈦奈米光觸媒(TiOxNy)。探討氮物質來源與濃度、合成時間與鍛燒程序對於生產之氮氧化鈦的性質影響。合成之氮氧化鈦粉末將利用X光繞射儀(XRD)、掃瞄式電子顯微鏡 (SEM)、紫外光-可見光分析儀(UV-Visible analyzer)進行材料特性分析(如結晶型態、表面型態與能階)。在實際光觸媒分解污染物之應用方面,由於亞甲基藍呈色容易且較易量測,將作為污染物用於做氮氧化鈦之初步效能評估。研究結果發現:摻雜不同氮源之氮氧化鈦光觸媒與純二氧化鈦結晶相似,且並未發現其他雜相形成。透過EDS N Mapping,可證實氮原子確實分佈在二氧化鈦上。本研究製備之不同氮源的氮氧化鈦可見光光觸媒的吸收範圍確實提升。其中,又以硫脲(Thiourea)為最佳,且其光降解效能最佳。

好「鉀」的溶液-鉀離子濃度的偵測

大鳳蝶衣櫥裡的祕密-大鳳蝶母蝶的型態研究

Swallowtail species, Papilio memnon heronus Fruhstorfer, demonstrates sexual dimorphism with four forms in females: melanism with tails, melanism without tails, albinism with tails, and albinism without tails. This study is to understand whether environment or genetics causes the differences. Besides, we hope to discover any possible link between characteristics of larvae and the morphology of adults. We understand it is the genetic factor that controls the expression of different morphologies. The two characteristics (body color and existence of tails) are controlled by two separate genes located on different chromosomes, and the inheritance pattern is consistent with that of Mendel’s law of inheritance. As for the observation in larva stage, we fail to notice any characteristics can indicate the future morphology of a particular larva. 本研究主要是在探討為何大鳳蝶雌蝶會有四種不同的形態:1.有尾白化2.有尾黑化3. 無尾白化4.無尾黑化,而造成此形態差異的原因又是什麼?探討造成此形態差異的成因分 為兩種:1.環境因子造成的2.遺傳因子造成的,我們也就是從這兩大方向去做實驗,對於環 境因子,我們的實驗設計是列出可能影響的因子(例:光照、溫度),而我們第一個探討的 因子就是光照,然而,後來發現有尾黑化的雌蝶,其子代在有光照及無光照的環境下皆有 無尾黑化、無尾白化、有尾黑化的雌蝶出現,而且可以從實驗很明顯的看出有尾的雌蝶, 生下無尾的雌蝶為多數而非定值,故我們可以確定造成此形態差異的因子不是環境,所以 我們又趕快從遺傳因子去做探討是何種遺傳類型造成的,實驗結果確定影響翅色及尾突的 遺傳皆為孟德爾遺傳。

味噌萃取物Soyasaponin I 抑制肺癌細胞轉移並且減少細胞激素分泌及抑制惡體質進展

研究指出Soyasaponin I 是味噌中的一種成分,其效果可以抗發炎,因此,本實驗想使用Soyasaponin I 探討其是否能應用於肺癌治療,及其對肺癌的轉移及癌症引起惡體質影響。 方式:使用肺癌細胞A549和H1299及正常的肺細胞HEL299進行WST-8試驗,測試Soyasaponin I 對三種細胞的存活率影響,用螢光試驗及免疫染色確認死亡方式,用Western blot及免疫螢光染色測試Soyasaponin I 對p-NF-κB入核的效果,進行boyden chamber模型測試Soyasaponin I 對於A549和H1299的侵犯速度的作用,並使用ELISA測出癌症引起惡體質的細胞分泌的IL-6細胞激素濃度。為了研究Soyasaponin I對於cachexia (惡體質)的影響,我們以人類脂肪組織利用原始培養出脂肪細胞,加入Soyasaponin I於脂肪細胞,以免疫染色研究。 成果:在細胞存活實驗發現高濃度Soyasaponin I 的濃度以細胞自噬引發癌細胞死亡,且不傷害正常肺部細胞,另外低濃度的Soyasaponin I 則使兩種肺癌細胞的突觸皆縮短及細胞變圓形;用Western blotting 證明Soyasaponin I 治療後mesenchymal的標記 (N-cadherin)明顯減少,而epithelial 的標記 (E-cadherin)明顯增加,接著在boyden chamber模型發現Soyasaponin I 會引發肺癌細胞發生間質-上皮細胞轉型,轉換成爬行較慢的上皮細胞型細胞; Soyasaponin I 減少肺癌細胞IL-6的分泌,抑制發炎。用免疫組織染色證明Soyasaponin I 治療後,原始培養脂肪細胞的惡體質標記 (UCP-1)明顯減少,減少棕色脂肪細胞形成,減少能量消耗及惡體質發生。

以黃色小鴨風潮探討高中生對療癒系物品特質與偏好之研究

本研究主要目的是以黃色小鴨的參觀風潮與商品特質,探討高中生對療癒系物品的偏好為何。黃色小鴨在全球形成一股風潮,許多人認為參觀黃色小鴨有紓壓的功能,也有人認為買小鴨玩偶陪伴自己,有療癒心情的效果,因此,本研究的主軸分別從「黃色小鴨的參觀活動」與「療癒系商品(HSP)特質」兩個大面向進行探討分析,釐清高中生對黃色小鴨療癒系物品(RDRP)的偏好為何。本研究對象為臺灣南部地區的高中生共254位,以「療癒商品與相關活動感受問卷」進行施測,分析結果顯示:(1) 對於療癒商品,女生喜好與購買意願均大於男生,其中又以「仿生造形型」類型最受歡迎;(2) HSP以「規律動作型」、「擬生命行為型」,而RDRP以「仿生造形型」、「手觸摸型」較能藉由放鬆及平衡情緒,達到療癒效果;(3) HSP與RDRP均以「聲控及感音型」較能藉由轉移情緖及產生驚喜,達到療癒效果。

A Modular Comprehensive Assessment Platform for Aircraft Maintenance

We were very curious about whether the aircraft will suffer lightning damages during flight, so we tried to search the answer on the internet. According to the searching results, we realized that during flight departure, passenger planes can suffer lightning damage. As a result, there will be lightning strike points, which needs immediate solutions for safety concerns. Besides, we found out that the exterior aircraft components, such as aircraft body, wings, tail, turbine engine and other areas, are vulnerable to corrosion, which also needs immediate solutions. Luckily, we came across a chance to chat with the engineer who works in the airport. Through that meeting, we knew that the maintenance of the aircraft is very important. However, the maintenance of the components depends on professional technicians, weather, the surrounding noise level, and other environmental effects. As a result, we think that it is initial for us to develop a device that can automatically complete the missions of aircraft maintenance. Below are two objectives that we need to complete: 1. Complete a non-destructive testing for aircraft damage, including corrosion and lightning strike points. Assessment areas include: Aircraft body, airplane wings, tail of the aircraft and the turbine engine 2. Engage in scanning results to analyze and predict for flight readiness. The collected results will proceed to the aviation company for inspection and maintenance. Based on these two objectives, we designed an automatic platform for aircraft maintenance. Below are four innovations of this platform: 1. we developed a method to replace the current stage based on the manual operation of the aircraft maintenance, the use of AGV (Automated guided vehicle) and the robotic arm combination. 2. Design a modular platform based on this method, including telescopic four-wheel independent rotating chassis and locking mechanism, scissors lifting mechanism, double sided synchronous belt forward detection telescopic mechanism, etc. The platform can shrink at the minimum height of A320, convenient access to the machine abdomen. 3. The positioning algorithm of the platform relative to the aircraft is proposed.

利用I.M.S.即時顯示系統建立資料庫,在重金屬污染監測上之應用

本研究以設計即時監測系統(Instant Monitoring System 簡稱 I.M.S.) 為目標,利用電解質導電原理,設計LED顯示系統,即時顯示土壤與河川受到重金屬污染。 電解質水溶液,在通電發生電泳運動時,不同的離子的水溶液電阻,會呈現出振盪的特殊性,可作為離子種類的判斷條件。藉由約105筆實驗數據,作七種重金屬離子的定性比對, 可以快速的比對出不同重金屬離子的濃度與種類。本實驗的設計與使用有以下的優點 : 一、 無論樣品電阻大小均可使用。二、 利用簡易工具,可輕易檢測出廢水內離子濃度的範圍與種類。三、 可作為檢測電泳與導電性質的輔助工具。四、 操作簡便,可廣泛使用。

反輪得行—胎痕軌跡關係辨析

本研究旨在探討轎車四輪關係。藉由車體結構的限制:左右互相平行,其距離為輪寬w,後輪沿車身延長輪距d,會碰到當時刻的前輪位置,以此做為發想,發展出前推後、後推前、左推右及右推左四種推論方式,最後得到結論。 研究最後將結論應用於許多方面,如應用於刑事鑑定方面,此外亦將程式寫於MATLAB以利修改跑跑卡丁車只留下了後輪軌跡之程式不足。

Stop the Spread of Desertification by Agar

The purpose of this research is to prevent the desertification by using my original “agar sheets”. The dry regions, in other words, the desert has already occupied about forty percent of the surface of the earth (Figure 1). In addition, it is said that land of seven million hectares turn into desert every year. However, we can reproduce the green-bosomed earth by using appropriate means, because this desertification originated in excessive farming, excessive pasturing, and deforestation caused by human beings. I learned “Cape Erimo’s Green Construction Method”, which has succeeded in planting trees in the coast of Japan by using seaweed, and this method led me to use the agar to prevent the desertification, which is a familiar Japanese food made from seaweed. I think that it is possible to prevent the desertification of any conditioned lands by using my original “agar sheets.”