永恆的旋轉木馬
本研究作品主要在探討「平面上各種曲線內關於相鄰等角割線段的新的不變量」與「空間中特殊圓錐曲面的特殊等角割線段的新的不變量」。 若圓錐曲線、蚶線等曲線中有相鄰等角的 條割線段,則這n條割線段之m次方和為定值。在圓錐曲線中這些割線段的交點可以是焦點、曲線內任意點,在蚶線中則為基點。甚至經由反演,還能將此性質推廣至直線上。 研究最後擴及至空間,先考慮特殊橢圓、拋物、雙曲球面,其一焦點為F,將正N面體VN之重心G與F重合,使得VN以F為旋轉中心任意旋轉,此時由F對VN之各頂點做射線交圓錐曲面於 PN,則FPN之倒數m次方和為定值,其中u=1,...,n,N=4, 6, 8, 12, 20 。
Investigating Novel Methods to Reduce Cholesterol Levels
An increase in blood cholesterol contributes to cardiovascular diseases, the number one cause of death worldwide. Statins are currently the most effective in reducing cholesterol levels and treating patients with high cholesterol. However, these pharmaceutical agents have been shown to cause several side effects, prompting the need for a more natural solution to increasing cholesterol levels. Hence, a study was conducted to investigate the ability of lactic acid bacteria in the removal of cholesterol, explore the mechanism for the removal of cholesterol by lactic acid bacteria, and examine the effectiveness of kidney beans and sunflower seeds in inhibiting HMG-CoA reductase in the cholesterol biosynthesis pathway. Results showed that Lactobacillus plantarum was the most effective in reducing cholesterol levels and that the mechanism for cholesterol removal included both the binding to cell wall and active uptake into cells. Sunflower seeds and kidney beans were also shown to be effective in inhibiting HMG-CoA reductase, with sunflower seeds having 100% inhibition of the enzyme, similar to pravastatin, a commercial cholesterol reducing drug, and kidney beans having comparable percentage inhibition of the enzyme compared to pravastatin.