全國中小學科展

四等獎

空間中的福特球

本研究旨在探討由法里數列生成的福特圓、以及與其有相似性,但是三維(或更高)的福特球的相關性質,我們分成三個部分來探討。一、首先我們驗證福特圓的衍生方式是否與法里數列相符合,並發想出另一種福特圓的衍生方法;二、以類似福特圓的方式,定義三維中的福特球、推導出以三顆球衍生第四顆球的公式、且限制其衍生的範圍,爾後由同一方向(以最新三顆球作衍生)、固定某一個球(固定某顆球,以最新兩顆球和固定球衍生)等方式衍生,並且利用空間中的索迪公式,對其半徑倒數與配合半徑倒數化繁後的x、y分子的遞迴關係式作探討;三、在高維度中,同樣定義出福特球(並非球體,只是敘述上方便的統稱),利用索迪公式對同一方向衍生的半徑倒數數列的遞迴關係式來探討。

AUTONOMIC HEATING GLOVES

In today's world, medicine is very advanced, thanks to which many diseases that were previously considered incurable, are now treated almost all over the world. But, unfortunately, some diseases are still incurable and can only facilitate their course. One such disease is Raynaud's disease or Raynaud's syndrome. Statistics show that worldwide the percentage of patients with this disease is 3-4%. Raynaud's disease is a paroxysmal spasm of the arteries of the fingers of the hand, rarely the feet when cooling the extremities. As mentioned earlier, this disease is incurable. That is why the creation of a device that can help people overcome many inconveniences due to the inability to stay in the cold without gloves or the problem of discomfort in heated gloves is relevant. And one of the solutions to this problem is to create special heated gloves. This work is also relevant, because even existing treatments, such as medication and conservative, do not completely solve the problem of reducing the sensitivity of the hands when cooled or even the slightest moisture on the palms. Also, these methods are very expensive, so our device will be cheaper and more affordable than existing ones. When using our gloves together with the two already mentioned methods, the treatment will be more effective. Unfortunately, medical and conservative treatments will lead to complications over time, so we not only maintain sensitivity in the hands, but also prevent further amputation of the upper extremities and the emergence of human health problems associated with the effects of drugs on the whole body. Nowadays, people work hard to be able to live well, but it is difficult for people with Raynaud's phenomenon to do so, as the sensitivity of the upper extremities decreases during the exacerbation of the disease. It is important for us to maintain the sensitivity of the hands by normalizing the thermal balance of the hands, which leads to the elimination of spasms of the atria of the hand. The aim of the work is to create a simple and effective means to normalize and maintain the thermal balance of the upper extremities, in order to reduce the loss of sensitivity of the hands in patients, as well as reduce the likelihood of spasms of the arteries of the fingers. The subject of the study is the course of Raynaud's disease and the current treatments for it. The aim of the study is the creation of special gloves that can stop spasms of arteries and maintain blood flow in them by balancing the heat balance in the hand, and depriving patients of the disease during their wearing During the work the following tasks were set: - to theoretically investigate the peculiarities of Raynaud's disease; - to analyze the existing clothes on the market with heating; - to develop and improve its own design of heated gloves, which will be affordable and easy to use. - calculate the cost of gloves taking into account all factors

太陽光熱分離的神奇之旅!

作品創新地利用空氣膠研製出太陽光熱分離器,分離後的太陽光與太陽熱再分別透過太陽電池作光轉電,以及熱電晶片作熱轉電。經由完整的實驗得到:(1)本作品小面積架構(5cmx5cm)在室內以150W鹵素燈模擬太陽能結合最佳空氣膠玻璃(濃度:2.5wt.%、厚度:0.08mm)、太陽電池模組、與雙邊熱電晶片模組之最佳結構可產出48.75mW的再生電能、(2)本作品小面積架構(5cmx5cm)在戶外用太陽能結合聚焦凸透鏡、最佳空氣膠玻璃、太陽電池模組、與單邊熱電晶片模組之最佳結構可產出174.5mW的再生電能、(3)本作品大面積架構(15cmx15cm)在戶外用太陽能結合聚焦菱鏡片、最佳空氣膠玻璃、可透光太陽電池模組、雙邊太陽熱轉電模組,除了成功應用在:微小電力儲能、風扇轉動、LED燈亮、及玩具車與機器人行走外,空氣膠玻璃的透光度至少88%且隔熱度至少12°C以上,不但有助於太陽電池的光轉電與散熱降溫,更實現節能與應用科學目的。

微生物發酵法運用於蚓糞處理與雞場除臭之研究

本研究以不同微生物發酵方式(EM菌(Effective Microerganisms)、枯草桿菌(Bacillus subtilis)、蔡十八菌、木黴菌(Trichoderma))養殖蚯蚓,並固定牛糞、紙污泥與太空包與其他輔料(米糠、蔗渣、果皮、腐葉)成分(原料來自雲林縣工、農業廢棄物),並用本土種的掘穴環爪蚓(Perionyx excavates)分解,以室內分層式堆肥採收蚓糞,再用機械篩選出高純度蚓糞;以雲林縣農作物:小白菜(西螺鎮)、香瓜(二崙鄉)、番茄(口湖鄉)為實驗作物,探討蚓糞當有機肥,作物生長與甜度變化;並將蚓糞與剩料(純度較低)運用於雞場除臭功能,經實驗結果顯示,蚓糞用於農作物與除臭皆有顯著的效果呈現。

狡兔八窟

科展源自於一個數學專欄上的問題,是關於兔子藏於圖形的某一個頂點,則在兔子位置可能變動和有所限制的射擊規則下,求出每一次最少要同時對幾個頂點開槍,才能「保證」可以獵到兔子。原始題目設定的圖形為正六面體,而我們將其擴展為不同的圖形,利用S(G)≥δ(G)+1得出路徑(Pn)、圈(Cn)的最小射擊點數,利用帶寬及|N(S)|相等的排序條件得出矩形(Pm×Pn)、長方體(Pm×Pn×Pk)、n維立方體(Qn)的最小射擊點數、利用觀察配合可行射擊策略,推測出完滿k元樹(k–treeh)的遞迴關係式並得出上界,建構可行方法,並期望算出最小射擊次數。目前研究結果為上述圖形之最小所需射擊點數及可行射擊策略。

以小鼠腎小管IMCD3細胞株探討纖毛生成和上皮細胞極化的關係

纖毛(cilia)病變是許多疾病的成因,像是多囊性腎臟病、巴德-畢德氏症候群等,但目前仍不清楚纖毛生成的機制。我們的研究初步證實纖毛生成和閉鎖小帶(Tight junction)可能有密切關聯性,且閉鎖小帶完整的細胞,纖毛基部到細胞底部的平均距離較長。因基體上的遠端附器(Distal appendage)能辨認細胞頂端膜(Apical membrane)上的特殊構造,有完整閉鎖小帶的細胞纖毛生長在細胞頂端,閉鎖小帶不完整時,細胞的極性未表現,纖毛無法生成在細胞頂端。 本研究以IMCD3(小鼠腎小管)細胞株,在去血清(serum starvation)的刺激誘導下,使IMCD3細胞長出纖毛,再以免疫螢光染色分析閉鎖小帶與生成纖毛的關係。並利用克隆形成試驗(Colony formation assay),將IMCD3細胞株分為四類型態,也進一步發現在三維培養中,四種細胞型態皆無法排列成空腔構造。最後我們建立載體DNA:pLAS2w.Ppuro-EGFP-Arl13B,以綠色螢光標示纖毛蛋白,在活細胞中追蹤基體的移動及纖毛生成的過程。期望藉由研究纖毛形成的過程機轉,能探討致病的作用機制,找出治療纖毛病變的療法。

Experimental Study on Pendulum and Self-designed Multi-layer-tank Water Damper for Mitigation of Structural Response

設計震動台和可調單擺模擬101大樓和調諧質量阻尼器的振動模式;並設計多層容器盛水與單擺比較,探討水深/容器長(Depth Ratio)、振幅、質量對減振效應的影響。實驗使用「振動參數」(週期、衰減係數、時間)量化減振效應。當單擺與震動台週期相近時,減振效應較佳。調整Depth Ratio使水自然擺盪週期(Tn)接近震動台週期(TV)(PR = Tn / TV≒1),易產生碎波,造成系統能量消散,減振效應顯著。震動台振幅越大,碎波發生可能性越高,減振效應越佳。當PR≒1,水質量變化對減振效應影響不顯著;若PR≠1,水質量越小,減振效應越差。實驗證實多層容器盛水的液體阻尼器可有效減振且效果優於單擺。

鉛直奈米皂膜之厚度變化

當皂膜鉛直立起後,其表面會因反射光形成干涉,利用反射光的干涉圖案可推知皂膜厚度。皂膜經單色光反射產生干涉圖案的數位相片,藉由Image J 自由軟體可分析出不同位置之光強分布,可回推對應之皂膜厚度。結果發現鉛直皂膜的側向結構具有3種類型的分布,造成這3種不同幾何結構分佈的微觀機制是因為皂膜中的微胞分布不同。 本作品將鉛直皂膜施以鉛直方向之外加電場,發現皂膜中的陽離子受到電力帶動周遭的液體運動,形成所謂的電滲透現象,電滲透可用來增厚皂膜。此種利用電場控制皂膜厚度的方法可以設計出奈米流體二極體,是一個嶄新的研究領域。

A New Approach to Recycling Aluminum/Iron Cans

本次研究提供一個更安全、效率、節省空間的回收鐵鋁罐新方法 - 扭轉。藉由預期圓筒在扭轉過程,對於固定半徑和長度會自發產生的摺痕數,事先在表面壓痕,一旦喝完飲料,只要輕輕一扭,馬上能將罐子安全地變扁,不用擔心割到手或罐子在踩壓時飛噴傷人。 我們系統地從實驗觀察和歸納不同半徑、長度、厚度、材料及拉伸力對於圓筒摺痕數目 (N)和偏斜角(α)的影響,並從幾何和能量考量,推導出符合實驗結果的簡單公式,得到不同參數下的擬合曲線,用來實際製作各種材料的回收模型。 由於日常容器有其他形體,我們接下來推廣到兩端半徑不同的圓筒和正多角柱。藉由實 驗數據及修正圓筒理論,得到較廣義的規律摺痕理論公式,預期同樣能夠利用此公式來設計摺痕;正多角柱與圓筒類似,在扭轉後產生規律的摺痕,只是數目和種類需要修正,因此也能夠利用扭轉達到壓縮的效果。

Synthesis of Biodegradable Plastic From Food Waste

Based on NEA Waste Statistics and Overall Recycling Rate for 2017, 809,800 tonnes of food waste and 815,200 tonnes of plastic waste was generated. Both food waste and plastic waste account for more than 10% of the total waste generated in Singapore in 2017 respectively. However only 16% of the food waste and 6% of plastic waste was recycled, the rest of it was disposed at the incineration plants and then the landfill. Such action will eventually lead to 2 major environmental issues that Singapore will face in near future: 1)Semakau landfill is our only landfill left and it is expected to run out of space in near future 2)The burning of food waste results in the release of methane (CH4), a greenhouse gas that has over 25 times the impact in trapping excess heat in the atmosphere as compared to Carbon Dioxide (CO2). This will increase carbon footprint and contribute to greenhouse effect and global warming in due course. According to the Sustainable Singapore Blueprint 2015, Singapore is working towards becoming a Zero Waste Nation by reducing our consumption, reusing and recycling all materials. A national recycling rate target of 70% has been set for 2030 with an aim to increase domestic recycling rate from 20% in 2013 to 30% by 2030 and non-domestic recycling rate from 77% in 2013 to 81% by 2030. As part of our total commitment towards waste management and sustainability effort, the purpose of doing this research project is to investigate whether food waste can be recycled and made into biodegradable plastics. First of all, chitosan will be derived from shrimp shells and be dissolved in acetic acid and lactic acid produced by probiotic fermentation of fruit and/ or vegetable waste for synthesis of biodegradable plastics.