攜手共解圓-扭結理論之探討
此篇研究發現在任何一個結中，都可以利用「牽手順序」和「交錯點編碼」兩種結的資訊直接看出一結化簡後的圖形。利用從「Reidemeister moves」所衍伸出的四種化簡方法{α, β, γ, δ}能更有效率的簡化結，並證明只需{α, β, γ, δ}就可化簡任何結，也利用{α, β, γ, δ}來驗證HOMFLY多項式是結不變量。由圖形及結的資訊我們發現，可使用「牽手順序」和「交錯點編碼」，搭配所討論出{α, β, γ, δ}的通式，依照步驟及通式簡化任何結。 本篇最重要的成果為：只需利用{α, β, γ, δ}即可化簡所有的結，而且比Reidemeister moves更有效率，因此可用{α, β, γ, δ}取代Reidemeister moves。 不管是一個封閉曲線或是兩個以上封閉曲線，都會遵守前述的規則，可利用{α, β, γ, δ}簡化圖形。文中也討論了較特別並具有規律的結──「星星結」，發現星星結只需使用「牽手順序」即可簡化，最後利用星星結的結論，發展出牽手遊戲中特殊的牽手遊戲情形。
Beets Revolution
There is currently an interest in developing supercapacitors as the booming of smartphones and other mobile electric devices. Despite offering key performance advantages, many capacitors pose significant environmental hazards once disposed. They often contain fluorine, sulfur, toxic transition metal and cyanide groups, which are harmful if discarded by using conventional landfill or incineration methods. The objective of this project is to find an environmentally benign alternative for building various key components of supercapacitors structures. From the electrolyte, carbon substrate and materials corresponding for Faradic reaction, all the materials were devised from renewable biomass. In our research, two novel designs of betanin/sulfonated carbon supercapacitor and quinone/sulfonated carbon supercapacitor were invented. Betanin and quinone, extracted from beets and Sencha, was preloaded on the sulfonated carbon nanosphere as the composite. While sulfonated carbon nanosphere were fabricated by hydrothermal synthesis of renewable biomaterial, followed by surface functionalization - sulfonation for increasing the loading capacity of nanoparticle. Nanostructured morphology and surface functional groups were examined and confirmed by SEM and IR spectroscopy. Specific capacitance can be boosted up through optimizing the particle size, morphology and surface polarity of carbon substrate and the type of electrolyte. From the experimental result, it is believed that the nano-architecture, with active functional groups, of carbon nanosphere enables the efficient charge transport and electrode stability, allowing the composite with high capacitance (94–209 F g–1 at a current density ranging from 1 to 4 mA cm–2), high capacitance retention of over 90% after over 20,000 cycles respectively, and over a wide range of temperature. Superior electrochemical performance of both betanin/sulfonated and quinone/sulfonated carbon supercapacitor can be attributed to the large accessible surface area of the porous structure, low interfacial resistance and its structural stability. It shows that they have relatively higher tolerant towards heat and extreme pH mediums. The green electrochemical capacitor exhibits a promising capacitive performance of 209 F g–1 with high capacitance retention of over 90%, opening up new possibilities for the production of environmental friendly, cost efficient and lightweight energy storage system using renewable biomass as the basic building materials without harming the environment.