全國中小學科展

2017年

多方塊的塗色問題

在本篇研究報告中,主要討論一個關於多方塊的問題:給定一個多方塊,試找出n的最小值使得在無限大的棋盤上,可以塗上n種顏色並且使多方塊沿格線無論如何放置,都不會蓋到重複的顏色。一開始先以V形三方塊的情況開始討論,之後將單方塊至五方塊的所有情況都有系統地討論完畢。 為了給出顏色數的估計,考慮同時適用於所有k方塊的情況。也就是說,要找到一個塗上n種顏色的無限棋盤使得無論任一個被選定的多方塊怎麼被放置在棋盤上,都不會覆蓋到相同顏色的格子。本篇研究成功地給出了此問題的精確解。 除了上面一種估計之外,本篇研究也考慮了矩形多方塊的顏色數,並試圖以之給出所有多方塊所需的顏色數之上下界。最後我得到k方塊所需的顏色數至多為8(k+1)2/25.

以線蟲動物模式評估漸凍人症之運動障礙

本研究探討TDP-43突變之漸凍人症(ALS)線蟲模式中的BLMP-1與其運動障礙之間的關係。在ALS患者的運動神經元內,Fas 訊息途徑活化之ASK1激酶被證實會導致軸突運輸障礙。在長壽漿細胞中,有研究發現BLIMP1可調控ASK1之表現。因此,本研究推測在TDP-43突變線蟲運動神經元中,BLMP-1(人類BLIMP1之同源蛋白質)會降低NSY-1(人類ASK1之同源蛋白質)表現,間接證明提升BLMP-1量有助改善癱瘓症狀。 本研究藉降低NSY-1表現的方式,分析線蟲之癱瘓程度與運動動能驗證Fas訊息途徑在線蟲中亦對運動功能障礙有顯著促進,確認其作為本研究模式生物之合理性。此外,將其側腹神經索中的BLMP-1表現量下降,發現其運動功能急遽惡化。最後將兩基因之表現量下降,則運動功能改善。 本研究首度證實線蟲之BLMP-1能有效的阻礙NSY-1所造成之運動障礙,且降低BLMP-1表達量會加劇其癱瘓症狀。此研究之發現對SOD1突變引起的ALS治療提供一個新研究方向及治癒的可能性。

Construction of an Emergency Portable Dynamo Mobile Phone Charging Station by Means of a Hand-Crank Gear Mechanism/ Solar Panels

The researchers aim to construct an emergency mobile phone charging station that runs on renewable energy and will serve as a cost-efficient alternative to more traditional power banks. Circuit components include a 20V / 6W solar panel supplemented by a hand-crank gear mechanism integrated with a 6V / 1A lead-acid battery, a usb output and an adjustable switch-mode power supply (SMPS) to convert excess voltage into current. Initial voltage and current outputs were measured under varying resistances. It was determined that the set-up satisfied the minimum voltage and current requirement for charging a mobile phone (5V / 1A). A subsequent phone charging test was executed using a Samsung Galaxy J2 (3.85V Li-ion battery 7.70W, Charge Voltage: 4.4V / 2000mAh) wherein it charged on an average of 0.277% per minute for the solar panel and an average of 0.263% per minute for the hand crank gear mechanism. A Mann-Whitney U statistical test was conducted to determine if the charging rate of the charging station had a significant difference from a commercially available power bank’s. The calculated UA: (4) from the test was below the lower limit and the UB: (217) was above the upper limit which indicated that there was a significant difference between the charging rates. While the efficiency was lower than the commercial power bank’s, it can still be used as an alternative charging method especially during emergencies and disasters.

EmerApp+: An innovative application for personal security

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.

Extracting Water from Humid Air Using Solar Energy in Humid Areas

The study aims to evaluate the technique of extracting water from humid air using solar energy through greenhouses in local areas. This technique is believed to provide limited amount of water in areas where potable water is not accessible or abundant. To solve this problem a pyramid-shaped device was designed, it is made of glass panels ad equipped with glass doors, fans operated by solar energy, and multiple shelves covered with fabric to act as Absorbent Calcium Chloride (CaCl2) with a 30% concentration. The doors are open during the night for absorption and closed during the day for energy-generating. Humidity, temperature, and atmospheric pressure are measured every two hours. The amount of water extracted in this area in one full day was around 3.0 liters a day for every square meter. Perhaps the limited amount of water is due to low level of humidity in the area: an average of 50% and temperature of F10 Celsius at night. However, the device itself is independent, does not need power sources, water sources, or infrastructure, can be installed in various places depending on humidity level as well as having the possibility of increasing number or size of device. This makes the device a promising, alternative and environmental friendly solution to produce water. Cost-effective and lighter material can be used to make the device, which will produce an easy-to-use and affordable devices. It is an area in need for further research to improve and further develop it.

故態復「蒙」,「日」新月異-Monge's theorem的性質探討與推廣

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。

Application of molecular templates on magnetic particles for adsorption and desorption of heavy metals

This study investigated the production of novel molecular templates, and analyze their adsorption effect on four heavy metal ions (Cu+2, Pb+2, Zn+2, Mn+2), which commonly exist in Taiwan's rivers. Different operating conditions (such as competitive adsorption, pH value and other factors) were explored to compare their adsorption effect of heavy metal ions by using the synthesized template molecules. The molecular templates were found to be specific towards their target metal ions with a high adsorption effect. Then combined with the idea of magnetic particles to produce magnetic molecule templates, a maximum amount of adsorption of heavy metal ions up to 95% through the molecular template was achieved while the effect of heavy metals desorption of up to 83% could be also successfully obtained. Experimental results showed that the magnetic molecule templates did not affect the adsorption of heavy metal ions. Not only can they speed up the recovery time of adsorption but the template molecules can also be collected more efficiently. We also proposed three different applications for the developed molecular templates. The development of magnetic molecular template may provide an affordable, highly-efficient way for dealing with heavy metal pollutions.

電場中的小晶靈-高電壓電場中液滴的結晶現象

本研究設計相機-顯微鏡-玻璃座平行銅片電場裝置,拍攝鹽類液滴在高電壓電場中的結晶現象,並以色階曲線為基礎,發展出SCL值,來偵測晶體表面的性質。實驗先找到能讓晶體成長趨向單顆且高透明的條件為:加蓋(低蒸發速率)、過濾、無施加電場與低熱LED光源。並應用蒸發速率差異,發現食鹽晶體的變速成長現象。蒸發快會形成階梯螺旋紋,蒸發慢,紋路消失,變成全透明晶體。將這裝置轉放在高電壓電場下可發現:晶體形狀發生改變(晶體傾斜或碎晶),透光度變差(SCL值變小),可觀察到新生晶體邊緣,有條狀暗紋出現,但晶體成長速率變化不大。鹽晶析出反應會因些微的外在變化,而影響溶液中離子堆疊,在晶體表面出現陰影或不規則紋路。這種對外在環境有著高度反應的現象,可以透過反應位能曲線圖來解釋,正可以用來研究外界高壓電場如何對物質發生影響。

自製高效率簡易水解發酵裝置將纖維素轉化為生質酒精之新製程

本研究以不同水解纖維素的方法,包括傳統酸水解、微波及臭氧法,完成效果比較,並以各方法最優勢理論組成最快速且產醣量最高的水解程序。再以麴菌發酵將醣轉為生質酒精,以止逆閥自製簡易即時取樣發酵裝置並研究效率最佳的麴菌酒精發酵,其中速發酵母平均一天酒精生成率高達約90.5%。 藉由基礎水解及發酵研究成功設計一套「低耗能、低成本、低汙染、高效率」自製可攜式簡易水解發酵膠囊進行纖維素水解,轉化為醣後又可在同一膠囊中加入麴菌進行酒精發酵,效果極佳,提升轉換率達63.8%。本研究進一步透過此自製膠囊推廣到廢棄稻草桿、甘蔗渣、甘蔗皮等,皆可得到極佳效果。

公益是否有價?── 論消費者背景變項與公益商品之關聯

消費者對於公益商品的訂價看法為何?利他行為會不會有價差?本研究採取隨機分派之問卷研究法,調查板橋車站內受試者所認為的合理公益餅乾售價。問卷分為兩個模組,分別為公益餅乾與非公益餅乾,消費者填答自己所認為的合理價格,並同時填寫性別、年齡、教育程度等等基本資料。 研究者將600份問卷排除遺漏值後,以584份數據資料進行迴歸分析。分析結果指出,年齡介於21到30歲之間的青年,最不願意為公益理念付出金錢,同時,教育程度越高以及感情狀態處於單身者也不願意為公益理念付出價差,而整體來說,受試者公益與非公益模組間的價差大約為平均價格的百分之十。研究者對此四項主要發現進行推論與探討,並期望日後有更多相關方面的研究。