BA-ADA based ROS-responsive nanoparticles for selective drug delivery in cancer cells
Current medical intervention in cancer therapeutic methods has shown risks and side effects with normal tissues. This includes incomplete cancer eradication. In reference to numerous studies and literature reviews, a stimuli-responsive drug delivery system is selected as an innovative, safe and more assured treatment due to its site-specific release ability. This allows specific intervention upon the given stimulus which response to the presenting disease symptoms. Hence, we designed a ROS(Reactive Oxygen Species)-responsive BA-ADA(4-Hydroxyphenylboronic acid pinacol ester and 1-Adamantanecarboxylic acid bonded molecule) nanoparticle delivery system. In our study, ROS-responsive nanoparticle was designed and prepared based on a synthetic molecule from BA and ADA. A therapeutic payload, Doxorubicin, can be loaded into the nanoparticles and it can be selectively released within cancerous tissues whereby ROS level is over-expressed. This will enhance both therapeutic efficiency and reduce side effects. The stability and ROS-responsiveness of the particle were proven in a series of evidence-based experiments. The results showed a significant difference in cell viability during the experiments with healthy and cancerous cell samples. Further research will be required to extend the experiment in vivo.
The Study of the Relationship between Global Warming and Acid Rain
The purpose of this project are 1)To study the relationship between global warming and acid rain with chemical model and mathematics model from temperature changing and pH of carbonic acid. 2) To create a pH measurement tool of carbonic acid in gaseous state.3) To study the impact of human activities in Loei province that affect to the relationship between global warming and acid rain. The procedures are 1)Do an experiment for studying the relationship between temperature changing and pH of carbonic acid. 2) Proof the mathematics model by using the result of experiment, the chemical reaction equation of carbonic acid solution. 3)Create a pH measurement tool of Carbonic acid by using Arduino and sensor with new formula in the computer program. 4) Using a pH measurement tool of Carbonic acid for studying impact of human activities in Loei province including industrial area, agricultural area, tourism area and forest area. The result of the mathematical model of the relationship between temperature changing and pH of carbonic acid is in form of Cubic equation in Equilibrium state and STP state. (Standard condition for Temperature and Pressure) So, we found that in this state has pH of carbonic acid is about 5.644. When the temperature rises up the effect of rainfall has a lower pH of carbonic acid solution. We also proof the new formula that create a pH measurement tool of Carbonic acid in gaseous state. The impact of human activities in Loei province found that the areas most affected by acid rain are the industrial areas, agricultural areas, tourism areas and forest areas respectively. In conclusion, when the temperature rises, it will dissolve acid solutions in the water on the earth. The loss of [H+] made the pH increases and the greenhouse gases become more atmospheric. These gases are more likely to react with atmospheric vapor. When these vapor form a cloud and condensation falls as rain, the rainfall has a lower pH, that is, global warming can result in the phenomenon of acid rain is greater.
Σn=1∞(n/(Cn2n))=√(x/(4-x)3) (√x(4-x) + 4sin-1(√x/2))與其相關的無窮級數
本文從一個博奕遊戲談起,探討遊戲的期望值得到一無窮級數Σn=1∞n/Cn2n 並嘗試用相關的數學概念與方法思考,首先處理問題Σn=1∞n/Cn2n 與Σn=1∞n2/Cn2n 的值,過程中利用了Σn=1∞n/Cn2n 函數與Σn=1∞n2/Cn2n 函數的性質將欲求之無窮級數轉化成積分或微分方程式的型態,再利用奧斯特洛格拉德斯基積分方法解出所求。 為了更有效率的得到相關之無窮級數,引進了微積分工具中之冪級數的概念,輔以微分方程式公式解求出了 f(x)=Σn=1∞Xn/Cn2n =√x/(4-x)3 (√x(4-x) + 4sin-1(√x/2)), x∈(-4,4), 進而推廣、延伸與其相關的一系列無窮級數,並利用導函數f'(x)求得 Σn=1∞n·2n-1/Cn2n的值。 接下來討論與f'(x)相關的無窮級數,發現可利用f(x)的高階導函數透過迭代方式得到Σn=1∞nm/Cn2n的值,其中m為任意正整數,歸納這些級數後可以應用在本文之博奕遊戲,讓獎金的選擇更富有變化性。 最後觀察f(x)與卡塔蘭數列{Cn}的倒數所構成之冪級數有所關聯,解出 Σn=1∞Xn/Cn的收斂函數後求出了Σn=1∞1/Cn的值以及{1/Cn}的偶數項與奇數項的和。
連續函數與多倍角公式推廣研究
本研究考慮的主要問題: 若非常數之連續函數f滿足∀m∈N,∃P(x)∈C[x] s.t.f(mx)=P(f(x)),其形式應為何? (一)、若考慮函數範圍為解析函數,則f(x)的形式必為下列三者之一: (1).axn+b (2). akx^n+b (3). acos(kxn)+b ,其中a,b,k∈C、n∈N (二)、若將考慮函數範圍改為:連續函數f:[0,∞)→C,則f(x)之形式必為下列三者之一: (1).axk'+b (2). akx^n+b (3). acos(kxn)+b ,其中a,b,k,k'∈C、n∈N、Re(k' )>0 (三)、若將考慮函數範圍改為:連續函數f:(0,∞)→C,則f(x)之形式必為下列四者之一: (1).alogx+b (2).axk'+b (3). akx^n+b (4). acos(kxn)+b ,其中a,b,k,k'∈C、n∈N 在本篇的最後,我們也將N的角色以其他正實數子集取代掉以推廣結果。
圓周上跳躍回歸問題之研究
圓周上相異n個點,將圓周分割成n段弧,每次每個點沿逆時針方向變換成與下一點所成弧之中點,若某點經m次變換後回到初始點,則m的最小值以及m的所有可能值為何?我們發現,m的最小值為n+2。更進一步發現,m的充要條件為m≧n+2且m≠kn-1, kn, kn+1,其中k為正奇數。接著,我們將問題一般化,圓周上相異n個點,沿逆時針方向變換成與下一點所成弧之p:q處,若某點經m次變換後回到初始點,則m的最小值以及m的所有可能值為何?我們發現,若p, q∈N,(p,q)=1,當變換次數r足夠大時,此n個點的位置會收斂至圓周上n等分點,同時,此n個點會在變換T=n(p+q)/(n,p)次後再次收斂至相同的位置。在這篇研究中,我們推導出任意點Pi變換r次後的點之位置坐標Ai(r)的一般式,不失一般性,我們針對P0求出A0(r)的最小極端值Lr與最大極端值Ur,在變換次數r足夠大時,透過觀察Lr與Ur對應到圓周上的收斂位置所形成的區間是否涵蓋原點,可預期P0變換r次後可否回歸。此外,我們也針對n個點具特殊初始位置座標來研究其回歸性質。