3D Arithmetic Billiards investigating edge points with a number theoretic approach
The billiard table is a cuboid with integer side lengths. A point-wise ball moves with constant speed along segments making a 45◦ angle with the sides and bounces on these. We allow the ball to start from any of the 8 corners, resulting in a periodic trajectory known as a corner path. The geometry of the path depends on the artihmetic properties of the side lengths (for example if these are pairwise coprime). Points of contact between the ball and edges, known as edge points, are inves- tigated and their characteristics like distribution explicitly described. This generalizes a previous work by Perucca, Reguengo da Sousa and Tronto of University of Luxembourg.
一價銠金屬催化肉桂胺衍生物進行不對稱氫芳基化反應
Rhodium(I)-Catalyzed Asymmetric Hydroarylation of Cinnamylamine Derivatives
一價銠金屬催化反應已經被廣泛應用於有機化學合成領域中。而本研究以具保護基之肉桂胺衍生物1與四芳基硼鈉試劑2a作為起始物進行銠金屬不對稱氫芳基化催化反應，得到具有保護基的掌性2,3-雙芳基丙胺衍生物3，並探討此反應的掌性雙烯配基對於反應的影響。本研究已完成使用Ts（對甲苯磺醯基）保護基之肉桂胺衍生物1a作為起始物進行反應，並改變與銠金屬錯合的配基，發現當配基使用2,5號位為芳基取代之配基L（掌性雙環[2,2,1]雙烯配基）時，反應有較好的位置選擇性，其中最佳的是芳基取代為苯基之配基L1，其位置選擇性比例為1:0:0.09。目前將進行改變起始物1之氮上的保護基，以L1作為配基進行反應，並與1a比較，優化反應性及產率。
Detection of Calcium Oxalate in Nephrolithiasis Using Ca-D
Nephrolithiasis isacommondiseasewherestoneisfoundinthe kidney. Kidney stones areharddepositsmadeofmineralsandsalts that form inside your kidneys. Urine has various wastes dissolved in it. When there is too much waste in too little liquid, crystals begin to form. Sometimes, tiny stones move out ofthebodyinthe urine without causingtoomuchpainanditcontainscalciumoxide. But stones that don't move may cause a back-up of urine in the kidney, ureter, the bladder, or the urethra. Therefore, Ca-d is used as an effective and affordable alternative device to check kidney stones. A new detector we can operate as an indicator for people who have high calcium oxalate levels in their urine. Which will help us to check calcium oxalate levels easily and practically with the use of tds (PPM as its unit). It can check whether people have high PPM levels that can cause issues like nephrolithiasis. It can also be used regularly so that people can avoid the disease by consistently checking their urine with Ca-d.