環狀網路的拓樸性質研究
In any , we prove that there exist cycles which have any length between 3 and 3n and paths which have any length between their smallest distance and longest Hamiltonian paths in any two different nodes; for any two nodes, there exist varied Hamiltonian cycles, making the two nodes locate on any possible counterpart position(only limited by the distance between the two nodes). In , there are 2n internally-disjoint spanning cycles, and 2n-1 internally-disjoint spanning paths. Besides, we also prove has no more than 2n disjoint spanning paths, and calculate its wide diameter.
本報告證明在環狀網路 中,存在有長度3到 3n 的所有迴圈;任何相異兩點都有各種不同的長度的路徑:從最短的距離到最長的漢米頓路徑;取定任意兩點,存在有各種不同的漢米爾頓迴圈,使得兩點位於所有可能的相對位置上(僅被兩點之間的距離限制)。在 中,也具有2n 個彼此不相交、經過所有點的迴圈,以及2n-1 個彼此不相交、經過所有點的路徑。除此之外,也證明了,在兩相異點間,具有個數不超過2n 且互斥的路徑,且這些路徑經過所有點。我們也估算了它的寬直徑。
懸浮奈米污染物之感測方法(Sensing of Nanopollutants with an Ionic Liquid)
由於奈米科技之進步發展神速,許多難以偵測的奈米污染物可能對生物體造成不可預知的負面影響,然而傳統之感測方法主要針對氣體分子,可能不適用於感測粒狀奈米污染物質。因此,本研究之主要目的是探討(也建立一套)奈米污染物簡易感測方法之可行性。利用二至三個塑膠瓶、塑膠管組裝簡易感測實驗,並且使用非常少量(約0.05 mL)之綠色溶劑(離子熔液),實驗結果顯示奈米ZnO 及螢光粉塵灰(2 或奈米CuO 反而使電阻增加;未通過過濾材料之螢光粉塵灰(2 and phosphor particulates was conducted in a home-made nanopollutant sensing system. Experimentally, abstraction of nano ZnO into the IL caused a reduction of the IL resistance. Similarly, decreasing of the IL resistance was also observed in the abstraction of phosphor particles with particles sizes of 2 particles was found. Abstraction of nano CuO in the IL also led to a slight increase of the IL resistance. The determined characteristic resistances of the IL for abstraction of select nano particles such as nano ZnO, nano CuO, nano TiO2 and phosphor particulates may be used in the development of novel nanopollutants sensors.