四等獎

奈米技術在 20 世紀後期蓬勃發展，而具有奈米及孔洞的超分子更為化學家所積極尋求合成上的突破與挑戰， 超分子化學用來探討一些分子間較弱、可恢復性的作用力，以期製備一系列具有功能性的孔洞材料 。 其主 要分為以下六種： 1. 凡德瓦力 (van der Waals forces，energy -1) 2. π-π堆疊作用力 (π-π stacking interactions ，energy= 0~50kJ‧mol-1) 3. 氫鍵 (hydrogen bonds，energy energy = 4~50kJ‧mol -1) 4. 偶極 -偶極作用力 (dipole -dipole interactions，energy= 5~50kJ ‧mol -1) 5. 陽離子-π作用力 (cation interactions， energy = 5~80kJ ‧mol -1) 6. 離子 -偶極作用力 (ion-dipole interactions，energy= 50~200kJ ‧mol -1) 而分子自組裝即利用這些作力， 依熱學最安定的合發生然排列現象可應用於分離、化學感氣體儲存子交換導熱以及光電性。 本研究主要利用混合掌性異構物的酒石酸鉀鈉與硝酸鈣或鎂，在水酒精的環境下進行自組裝，利用簡單與無毒的自組裝合成法，讓右旋酒 石酸分子鎂金屬配位而左石酸分子與鈣金屬配位，別得到掌性聚合物除了將兩種 掌性異構物分離，也 實踐綠色化學中無毒與環保的概念 。

本文主要在探討幾何中的兩個重要結果—三角形中的『孟氏定理』與『西瓦定理』推廣到平面上任意的『凸 邊形』與『凹 邊形』的相對應結果，甚至於我可以將『凸凹 邊形』換成『 條直線』，我發現亦可以得到類似的結果。在完成平面上的圖形推廣之後，我也試著思考其在立體空間中是否也有類似的推論，很幸運地也發現有類似平面多邊形的結果，目前已完成空間中任意『 個頂點多面體』的『孟氏共面定理』；此外，我也證明了空間中任意四面體的『西瓦共點定理』，同時以實例驗證空間中的『西瓦共點定理』在四角錐中的形式，進而找到『 個頂點多面體』的『西瓦共點定理』之形式，並已驗證其正確性。

Autonomous car is a very new concept, being a car without any driver. Several concurrent software process data using Artificial Intelligence to recognize and propose a path which the car should follow. The goal of the project is that a driverless car can reduce the distance between the cars, lowering the degree of road loadings, reducing the number of traffic jams, avoid human errors, and allowing people with disabilities(even blind people) to travel using an autonomous car. Theoretically a car without driver in the future should be much safer, because human reaction speed is higher than 200 ms, and the computing power of the newest computers allows traffic calculations even to 10 ms. The necessary power is provided by three multi-core laptops that process with Artificial Intelligence in order to recognize traffic signs, traffic lanes , traffic car fingerprints, processing the data from a 3D radar, using particle filters to localize car in a GPS map, the management of database with traffic signs, magnetic sensors, acceleration sensors, a distributed software, a supervisory system and the software which drives the stepper motor to turn the steering wheel (acceleration and braking). Currently the software is able to recognize the traffic signs, register them in a database using Google Maps. The fields record the sign and direction of travel from that area. Each car participating in the traffic and using this software will register new signs detected and the will modify the degree of confidence of recognition for other users. Another software component is able to recognize the demarcation lines between lanes, with three cameras to calculate exactly or using probabilities where it is on the road, where the roadsides are and to propose a new direction even in the absence of traffic signs for the next seconds. Another part of the software is trying to use Artificial Intelligence to detect other car fingerprints from webcam images. The calculation was performed on 3 computers, requiring distributed processing. I developed a management information system based on semaphores that allows data processing and supervision from 3 different computers. This project presents a hardware version of a LIDAR – a 3D radar and a software for creating a 3D environment in which the car navigates and using it the car will take decision to avoid obstacles. The LIRDAR contains a total of 16 avalanche photo-detector mounted on a stepper motor that spins at a frequency of 10 Hz. The information provided by my radar is about 576.000 pixels at resolution of 10 bits. The 3D radar helps the entire software system to increase the confidence of decision.

本文是利用整數分拆及排容原理研究以1x2 矩形鋪mxn 矩形的排法邏輯及總排法數，並進一步探討下列兩種情況：雙邊不含缺陷線及至少有一缺陷線的排法數。\r Based on the Apart of Number and the Inclusion- Exclution principle, this research intends to analyze the logic and final result of permutation by laying an 1x2 rectangle over an mxn rectangle. From the analysis, this study will go further to explore the possible permutation in the following two situations : when there is no fault line on both sides and when at least one fault line exists.\r

Dye-sensitized solar cells (DSSCs) have cheaper and easier means of fabrication compared to the currently used solar cells, which are mostly silicon-based, so DSSCs are developed for a prospect of solar energy accounting for a higher percentage in the world’s total energy production, which is currently 0.1%. However, compared to their inorganic counterparts, their efficiencies are low, and the search for a dye that will maximize the potential of DSSCs is still ongoing. The aim of this study is to be able to evaluate the absorption range in the solar spectrum of dyes extracted from Basella alba leaves and Bixin orellana seeds, and of dyes resulting from the mixture of both extracts, using UV-Vis Spectrophotometer, with the objective of increasing the absorption; to be able to fabricate functional DSSCs from the individual and mixed dyes; and to be able to evaluate the different conversion efficiencies of the DSSCs of the individual and mixed dyes using Linear Sweep Voltammetry, with the aim of increasing the conversion efficiency due to a wider absorption range. B. alba leaves and B. orellana seeds were extracted using soxhlet extraction. The clean extracts were mixed in different proportions, and were characterized using UV-Vis Spectrophotometer. The two individual dyes together with two proportions of the mixed B. alba:B. orellana dyes, 1:1 and 2:1, were then incorporated into DSSCs. In the fabrication of DSSCs, twelve plates of Fluorine doped tin oxide were coated with titanium dioxide (TiO2) using spray pyrolysis. They were sintered and scraped, and were afterwards immersed in the four dyes for four days. Platinum plates were placed on top, and iodine-triiodide couple electrolyte was introduced via capillary action. The sealed DSSCs were subjected to Linear Sweep Voltammetry under dark and illuminated conditions, using a sun simulator. Results from the UV-Vis spectrophotometry showed that mixing the dyes had increased the absorption range of the individual dyes, although not superpositionally, and that the 2:1 mixed dye has the most potential. Being incorporated into DSSCs, the dyes, including the mixed ones, have successfully converted solar energy into electrical energy, as shown by the significance in conversion efficiencies under dark and illuminated conditions. However, despite the increase in the absorption range, neither of the mixed dyes have shown a higher conversion efficiency than the individual ones, which can be accounted for a possible weaker interaction between the two dyes and the TiO2, resulting to lower efficiencies. The study has been able to obtain and characterize dyes from B. orellana seeds and B. alba leaves and has been able to incorporate the dyes into DSSCs. With the wider absorption range of the mixed dyes, the study has been able to confirm the possibility of the dyes to maximize the potential of DSSCs, as shown by the successful conversion of solar energy into electrical energy of all fabricated DSSCs, including those of mixed dyes. If the possible problem with the dye-dye as well as the dye-TiO2 interactions could be solved, the possibility of much higher conversion efficiencies could be expected.

The purpose: To study the basaltic prisms to understand their formation. Tasks: To study chemical and mineral composition, textures and density of basalts of central and peripheral parts of prisms, to reveal the possible difference as a consequence of the formation of Benard sells. Basalt prisms have 6-5-4-face shape with a diameter 10 -50 cm and height of 30-40m. They are divided by transverse fracture in blocks of 20-50 cm. Prismatic jointing of basalts widespread throughout the world. There are many theories about its origin. We decided to collect data to identify the most appropriate of these. We suppose that if the hypothesis about the role of Benard cells is correct then the properties of basalt in the central and peripheral parts of the prisms must be different. If we consider the center of the prism as the center of the cell, where the hot matter rise, spreading out to the periphery and lower in the peripheral part, it is likely that the density of basalt forming in the center must be lower than at the periphery and later crystallization should lead to a slightly more acidic basalt in the middle. We determined the density of basalts of different parts of prisms. And the density of central part basalts was equal to 2.502g/sm3 and of peripheral part basalts was equal to 2.907g/sm3. X-ray fluorescence analysis showed that basalt of central part contain 12,91% Si and of peripheral part only 10,17%. Basalt of central part is depleted of Fe, Mn, Ti, Mg compared with of peripheral. We investigated samples and thin sections of basalts under the microscope MIN-8. For basalts of peripheral part flow texture expressed by the orientation of the microlites are characteristic. In the central part flow texture are poorly expressed but we can see many phenocrysts. Our data reveal a significant and expected difference between the basalts of central and peripheral parts of prism, that are the evidences in favor of the hypothesis about the role of Benard cells in the formation of basalt prismatic jointing.

本研究接續去年的研究主題”驚奇的數”，邊長為平方數的三邊形數亦為四邊形數的問題。解決這個問題後，利用Pell方程式與矩陣計算來求哪些邊長的p邊形數亦同時為四邊形數。處理方法分為兩類：第一類可以使用矩陣計算來討論，已討論出附帶方程式部分的初始解情形，並嘗試改進矩陣計算的漏解問題以及對數據做詳細分析、歸納。目前已有兩種方法：1.放寬附帶方程式初始解的限制，也就是縮小遞迴式的係數；2.伸縮雙曲線為一套固定的方法，可以解出原矩陣計算所遺漏的解。第二類無法使用矩陣計算，利用因式分解的技巧處理，發現結果與切比雪夫多項式有著密切關係。

Characterization of telescope lenses using physical optics and selection of the optimal physical parameters of a reflecting telescope’s optical units were done to improve the design, cost-efficiency, and quality of the 64-cm telescope (named Oof) housed at the National Institute of Physics. Characterization has been done through numerical modeling of the point spread function (PSF) in Python. The PSF code was based on the method of getting wave vectors by Richards and Wolf. The optimal PSF was established to be the PSF of a large monolithic mirror. The PSF of a single optical lens was compared to its counterpart segmented lenses. Through the comparison of maximum intensity, the normalized mean square error (NMSE) and the Linfoot’s criteria of correlation quality, fidelity, and relative structural content, the study has produced results which proved that highly segmented optical components produce results with less quality compared to less-segmented optical components. It was found that as the segmentation increases, the maximum intensity decreases. Higher values of maximum intensity denote higher light gathering power. The normalized mean square error of the set-ups having one to seven layers had values greater than zero but less than one. This denotes that the PSF of those set-ups are near the PSF of the optimal set-up. Higher values of correlation quality, fidelity, and relative structural content denote higher correlation, higher signal to noise ratio, higher closeness of correspondence between the optimal set-up and the segmented set-up. The number and the size of the optical components of the segmented mirror were manipulated in order to achieve a negligible difference between that of the optimal PSF and the PSF of a segmented mirror. The equivalent single lens radius in terms of maximum intensity of the current set-up of the telescope was determined to be 234.25 mm. If the optimal PSF is achieved, the physical parameters of the optical components generated may be applied to the optical components of the 64-cm telescope. The design that resulted from the study could be used in the future construction of a wide-aperture telescope, which could aid in the acquisition of knowledge about heavenly bodies.

低頭族發生『假性近視』、『脊椎側彎』甚至『黃斑部病變』等健康問題有越來越多的趨勢，邊走邊玩發生的意外也越來越多，因此，我們針對低頭族的健康與安全開發本作品。一、 健康方面： 撰寫「背景執行程式」，此程式完全不影響使用者玩遊戲、上網…等等，使用30分鐘後，透過「加速度感測器」檢測使用者必須做的手臂運動，完成後才可繼續使用手機，藉此『休息一下眼睛與僵化的手臂』。透過「環境光感測器」調整螢幕亮度，不讓螢幕光太強而造成眼睛更容易損傷。二、 安全方面： 「加速度感測器」與「陀螺儀」辨識出使用者邊走邊使用手機，就跳出提醒視窗暫時中斷使用者使用手機，使用者或許就會停下腳步或是抬起頭來恢復對環境的觀察能力以避免意外發生，按下「確定鈕」後，就可繼續使用。

在沙灘賣冰問題中，假設遊客平均分布在長度為1的沙灘上，並且沙灘上的攤販不論品質或價格都相同。因此遊客只會依據距離遠近選擇攤販；攤販則會為了擁有最大客源而不斷移動，直到任何移動皆不會使利益增加為止，這就是所謂的奈許均衡。 已知兩個攤販會集中在沙灘正中央，而三個攤販時無法達到均衡，四家或五家攤販會形成唯一一種均衡，若有六家以上的攤販則可能有不只一種均衡。由五家攤販的例子我們觀察到，若是選擇在1/2處固定不動，當其他四家攤販達成均衡時，就可以分得最大的利益範圍。因此，我們試著在三個攤販的情形中固定其中一家攤販的位置，發現若其中一個攤販在1/4的位置固定不動，則剩餘兩個攤販會集中在3/4形成均衡。此時固定攤販可以分得1/2，其餘兩家則各得1/4。於是在接下來的研究中，我們試著將此發現推廣至一般性。 我們研究發現，固定攤販的設攤位置，可以決定奈許均衡的存在性──使沒有均衡的例子產生均衡，或者破壞原本有的均衡；亦可以影響均衡的型態。最後我們提出了一個保證獲利的策略，使得採取適當的固定位置必定得到優於平均的利益。同時也證明了此策略為固定攤販獲利最大值(Max Minimum)，成功的將固定攤販利益最大值的情形推廣至一般化，並歸納出固定攤販位於各範圍時所形成的均衡以及利益範圍。