Improving Communication for the Visually Impaired Through an Innovative Arabic Writing System
Visual impairment is a major global health problem. In 2017, WHO estimated that there were 253 million people worldwide with this ailment. According to the journal of the American Medical association, the prevalence of visual impairment in the Saudi population is 9.3%. Learning Braille by families of students with visual impairments remains a major obstacle, which precipitates several communication issues. Moreover, difficulties for the students themselves lie in learning braille with languages that include diacritical marks; consequently, affecting their academic progress. My main objective of this project is to help improving life quality of these individuals, and the focus is to advance their social productivity and adaptation. This was accomplished through creating a new simpler Arabic writing system using geometrical shapes. As a part of this project, fifteen participants with visual impairments were interviewed and tried this new writing system; two of them are adults between 25 and 40 years old while the rest are students from 9 to 17 years old. Additionally, 100 participants with visual impairments completed a survey. The data showed that students learned this system in two hours in comparison with students that mastered braille in a few months. This shows that this system is easier to learn and subsequently saves time and effort. The most important value added to this project is that diacritical marks were combined with the alphabet, thereby considerably reducing book sizes compared to Braille-written books. This project presents a novel system that helps people with visual impairments to increase their confidence and independence.
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。
Improving Spinal Fusions: Redesigning the Pedicle Probe to Prevent Vertebral Breaches
Pedicle probes are medical devices used by surgeons during spinal fusions for patients with conditions such as scoliosis and spinal fractures. The probe creates pilot holes to guide the placement of pedicle screws in vertebrae. The screws are then connected with a metal rod to stabilize the spine. Twenty-nine percent of patients who undergo spinal fusions suffer from vertebral breaches – accidental damage to the spinal cord – which cause complications such as infection, motor defects, and in many cases paralysis. My goal was to make spinal fusions safer by redesigning the pedicle probe to provide surgeons with instantaneous feedback on the probe’s location, enabling them to more accurately place pedicle screws. The pedicle probe I developed takes advantage of the difference in density between the inner cancellous (spongy) bone and the outer cortical (compact) bone found in vertebrae. Cortical bone is avoided by monitoring the cannulation force – the force required to insert the probe. When the probe contacts denser cortical tissue, it warns the user by providing tactile and visual feedback through a vibration motor and an LED. This enables the surgeon to redirect the probe and advance down the optimum path, preventing a possible breach. It proved successful in preventing breaches on lamb vertebrae, which closely resemble human vertebrae. This novel device improves feedback to the surgeon and eliminates the need for costly and potentially harmful ionizing radiation exposure. Furthermore, it does not depend on, or require, any preoperative imaging. The cost of manufacturing the improved probe is less than $42 USD (NT$1297). Results of patent searches for 加拿大, the 美國, and Europe suggest that the redesigned probe is unique in predicting and preventing breaches in spinal fusions based on predetermined force threshold values. The probe is also unique in enabling personalized procedures in spinal fusions for those with complications, through calibrating a control (force) limit based on tissue samples prior to the procedure. Enhancing a surgeon’s ability to determine an appropriate path for pedicle screws through a sensor-enabled probe has the potential to significantly reduce the incidence of vertebral breaches during spinal fusion surgery.
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。
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.
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。