二等獎

用塑膠軟管作為氫爆安全反應器，從封閉端點燃氫氧預混氣，管中火焰\r 傳遞快速，肉眼難以觀察，因此研製「氣爆顯影記錄器」來觀測，如下圖，\r 光纖導引偵測點的火光至暗箱，記錄於高速旋轉的軟片，從光電轉速計讀取\r 轉速，軟片沖洗後量測各顯影間距，可得火焰位置與時間的關係圖，量測時\r 間最小刻度可達2. 2 微秒。\r 解讀軟片的顯影，得知氫爆初期，火焰加速傳遞，大部分在25cm 位置\r 左右，火焰的速率出現急速飆升(爆燃轉變為爆震)，而且火光亮度也急速升\r 高，有時火焰速率出現飆升過高，再回降趨於穩定?的現象，在50 cm 位置\r 左右，火焰進入等速傳遞階段，此階段有穩定的火焰模型，火焰頂端的亮度\r 最高，往後亮度遞減。

本研究以網路上Soft X-ray、UV195Å、K-Line、Ｈα波段太陽影像上黑子，光斑經度位置的逐時變量，試求太陽自光球層以上各層是否有越高層轉速越慢的現象？經試用數種方法求大量黑子、光斑位置，最後以省時，且誤差減小的＂由PhotoShop軟體讀出黑子、光斑在圖檔中位置，於EXCEL軟體中套用日面座標公式＂，以Peter Meadows的黑子定位程式抽樣對驗，來求其經緯度值。結果：在任何緯度，光球層以上各層轉速不同（徑向較差自轉現象），但並非越高層越慢，而是在大部分緯度處其各層速度變化呈 的快慢交替現象。

此研究的目的是要設計出一套完整編輯顯現數學式、加以計算，並求出解的一套方法與成品。而這項工作的執行者，在此稱之Equatetor 。一般的數學式子，若要計算的話，普通的計算機是不足夠的。原因是它們沒有辦法表現出數學式的「原貌」，例如分號、指數、函數、根號等數學符號混在一起時的情況。於是，我便擬定了一個研究，希望設計出一套更方便且實用的方法。換句話說，我要設計出一個功能強大的工程計算機程式。其中，自然牽扯到數學式子的顯現方式（以MathML 實現），以及計算機科學的演算法及資料結構。我主要的目的有四：(1) 顯示數學式(2) 方便編輯數學式(3) 計算數學式(4) 處理可以以不同形式輸出解答的計算（如輸出分數、根號、函數解等）。研究結果中，成功地運用XML 中的MathML 與二分逼近分數等演算法及若干資料結構，達到了以下實用的幾點：(1) 結構化的數學式編輯(2) 完整地顯示數學式(3) 正確運算並輸出運算式的答案(4) 提供一般數學形式之解（非小數之解）;The object of this study is to design a method and processor which is able to edit, display a mathematical expression representing a number, calculate and output the answer. The executor of this task is called Equatetor. Normal calculators are not adequate for this kind of task. The main reason is that they can’t reveal the original expression, such as fractions, radicals, exponents or mathematic functions. Therefore, a simple and convenient method is needed. To perform the possible way of handling those tasks, a computer program has been written. Several techniques were used, such as MathML, computing algorithms, data structures, and so on. Following are main purposes: (1) Displaying mathematical expressions. (2) Editing mathematical expressions simply. (3) Calculating mathematical expressions. (4) Outputting the answers(in different expressions). And the achievements:(1) Structured methods of editing of mathematical expressions. (2) Displaying mathematical expressions completely. (3) Calculating mathematical expressions precisely. (4) Offering answers in different expressions.

在模式植物──阿拉伯芥（Arabidopsis thaliana）中，AtYAK1（Arabidopsis thaliana Yak1-related protein kinase）是目前發現唯一屬於DYRK（Dual specificity Yak1-Related protein Kinase）的蛋白激?。雖然之前研究已證明，不同物種之DYRKs 和細胞的生長與發育過程有關。然而，其在植物中的生理功能卻尚未被明確地研究報導過。在先前的研究中，為瞭解AtYAK1 在阿拉伯芥內作用之位置，前人選取AtYAK1 基因ATG 上游約2.5 kb 的序列（Upstream Element, 2.5KUSE）建構至一含有GUS（β-glucuronidase）報告基因的質體中，並轉形至阿拉伯芥，進行GUS 組織染色分析。但在初步結果中，並沒有在轉殖株觀察到明顯的GUS 表現。進一步分析，我們發現在2.5KUSE 序列末端約0.5 kb 的5’非轉譯區（5’untranslated region, 5’UTR）中，有四組開放讀序框（Upstream Open Reading Frame, uORF）。有趣的是，許多研究也顯示，uORFs 會影響轉譯過程中的再起始（re-initiation）作用而調控該基因的表現。另一方面，前人亦透過構築好的2KUSE 轉殖株（即不含有5’UTR）進行上述GUS 實驗。結果發現，此2KUSE 轉殖株的GUS 表現非常顯著。本實驗即要瞭解AtYAK1 的uORFs 是否也會影響其蛋白質的合成。首先，我們以點突變的方式將四組uORFs 中之ATG 換成TTG，目的為構築不含有uORFs 之5’UTR（mutated uORFs, ΔuORFs）。在進行原生質體短暫表現分析法（protoplast transient assay）及GUS 組織染色分析後，將結果與含有uORFs 的結果作比較：當缺乏uORFs 後，其3’端報告基因的表現量確實比原來顯著。綜合以上，我們認為此uORFs 對於AtYAK1 蛋白質之表現佔有相當重要的影響地位。最後，我們對5’非轉譯區是否存在開放讀序框進行阿拉伯芥全基因組分析，相關結果亦於本研究報告中分析討論。AtYAK1（Arabidopsis thaliana Yak1-related protein kinase）is the first DYRK（Dual specificity Yak1-Related protein Kinase ） family member identified in the model plant ─ Arabidopsis thaliana and exists as one copy gene in Arabidopsis. Previous studies showed that many eukaryotic DYRKs are involved in regulating the growth and development of cells. However, the study of AtYAK1 in Arabidopsis is lacking to date. In order to understand where AtYAK1 expresses and functions in plants, a 2.5 kb fragment which is located upstream from the major ATG of AtYAK1（termed Upstream Element, 2.5KUSE）was previously constructed to drive the expression of a reporter gene, GUS（β-glucuronidase）, in transgenic Arabidopsis. Much to our surprise, no GUS expression signal could be detected in such transgenic plants. When further analyses were performed, we found that there are four upstream open reading frames （uORFs） in the 5’untranslated region ( 5’UTR ) within the 2.5KUSE. Many studies indicating that the uORFs can regulate the translation of downstream ORF encoding the major gene product through the procedure of translation re-initiation. This action represents a mode of translational regulation for gene expression. Indeed, GUS activity could be readily detected in transgenic plants expression 2KUSE::GUS, a construct lacking the 5’UTR of AtYAK1. In this study, I have tried to elucidate whether the uORFs of AtYAK1 can regulate the translation of the downstream major ORF. First, in order to construct a 5’UTR fragment of which uORFs have been mutated（ΔuORFs）, we apply site-directed mutagenesis to substitute ATG with TTG for the four uORFs and examine the expression of GUS driven by this mutated 2.5KUSE. After analyzing the results in both Arabidopsis protoplast transient assay and transgenic Arabidopsis, stronger expression of reporter genes in both systems were observed when the four uORFs were mutated. We have also confirmed that, in transient expression system, the increase of reporter gene activity was not due to the excess accumulation of the corresponding mRNAs. Rather, it is the four uORFs which play an important role in negatively regulating the translation of AtYAK1, possibly via inhibiting the translation re-initiation of major ORF. A genome-wide examination of uORFs in all Arabidopsis genes was also performed to assess the possible contribution of uORF in regulating gene expression.

Cultures of bacteria were analyzed using fractal geometry and statistics to provide a method for predicting organism growth, paving the way for a better design of treatment drugs. Images of three cultures of isolated Bacillus subtilis were taken at time intervals of two to three hours for eight days. The images were processed using the IDOLON program and quantitatively described using three statistical formulas: fractal dimension D, Renyi dimension and Hausdorff-Besicovitch dimension. The three variables were integrated to compute the maximum of the distribution and were used as coordinates for a 3-dimensional graph f. A 2-dimensional graph g containing the maximum of a distribution under time analysis was also constructed. Topological properties of the graphs, including slope, direction and area were used to determine the interrelationship of the three fractal values. The two graphs, described as φ - : X -? P1 where X is the smooth algebraic assimilation of the four variables under time analysis, was extended using Java. A computer-aided prediction model of the graphs f and g were made which combined the topology of f and g at infinity. The computed fractal values showed the existence of a fractal pattern in the growth of Bacillus subtilis with fractal dimension ranging from 0.900 to 4.000, indicating a linear iteration. This was supported by the values of the Renyi dimension, which showed a horizontal growth pattern of the bacterial cultures, establishing the growth of the bacteria to be inclined to go towards the North East direction. There was consistency in the computed fractal values, maximum of distribution and topographical computations of all three cultures which also indicated the existence of a pattern of growth which could be extended to tinfinity, thereby allowing prediction of the direction and rate of growth of the bacterial colonies. The fractal patterns in the growth of bacteria, in this case Bacillus subtilis, yielded the direction and rate of growth of the bacteria as shown by the analysis of the fractal patterns and statistical values, showing that the growth of harmful organisms can therefore be predicted, making it possible to improve on the design of drugs for the control of perilous cells. By preventing the growth of insidious cells, the potential effects of virulent organisms may be avoided, and treatment may be made more possible.

Nano-sized calcium phosphate was used in the synthesis of starch-based composite plastics to provide a cheap but sturdier biodegradable alternative to petroleum derived plastics used in film packaging. Nano-sized calcium phosphates were produced from the precipitation reaction of calcium nitrate tetrahydrate (Ca(NO3)2 ‧ 4H2O) and phosphoric acid (H3PO4). The nanoparticles were co-extruded and molded with thermoplastic starch (TPS) at ratios of 0%, 1%, and 5% by mass. Tensile strength and elongation percentage of the resultant composite plastics were tested in three replicates. The results show that there is a significant difference between the tensile strengths of the 0% and 5% calcium phosphate composites at a 5% level of significance. The trend between the composite’s tensile strength and percentage calcium phosphate follows a geometric progression, enabling a projection for the 10% nano-calcium phosphate to have a tensile strength of 10 MPa, the average tensile strength for low-density polyethylene (LDPE). This shows that it is feasible to synthesize a 10% nano-calcium phosphate-TPS plastic that can be a viable substitute for LDPE plastics in film packaging, paving the way for the commercialization of starch-based plastics. The use of biodegradable plastics with improved physical characteristics will lessen consumer dependence on petroleum derived plastics and solve the environmental issues brought about by the use of such plastics.

目前警察機關採用酚酞法檢驗有無血跡存在的可能性，我們希望研發新的試劑取代酚酞以增加靈敏度。 研發實驗分為四個階段： 一、 定性階段：實驗何種指示劑可取代酚酞法，檢驗有無血跡存在的可能性。 二、 定量階段：實驗新試劑與雙氧水之最適比例以及新試劑與不同血液樣品之反應速率比較。 三、 靈敏度比較階段：實驗亞甲藍法與酚酞法在不同濃度樣品的比較。 四、 反應機構推論階段：由實驗推論可能的反應機構並由新試劑之結構探討可能的反應機構。 實驗結果顯示，我們已成功地找到新的試劑（亞甲藍）作為初步血跡預備試驗。亞甲藍除了較容易配製、顏色不易與血液混淆，且在檢驗有無血跡時，其靈敏度亦較酚酞法高，以上優點證實此新試劑亦可做為血跡檢驗之用，作為初步血液預備檢驗。

Electrocardiograms are important medical devices used to monitor the cardiac activity of patients over a period of time. Designed to provide convenient monitoring of patients, although most useful, ECG’s however are expensive and usually not portable, limiting its availability and therefore usefulness. Taking advantage of current technological developments, the researchers developed an ECG System with Androidâ„¢ smartphone based monitor, and Bluebeat© ECG Front circuit based electrodes. The system is divided into two, software and hardware interface. The developed software interface code used an Android based Java language which displays the converted ADC values in the LCD. Saving and user friendly features were also included in the smartphone. The hardware interface is composed of the ECG front and the Data Acquisition Module. The ECG front contains the filters and amplifiers that will receive the human cardiac signal. The DAT Module will then receive it with its Gizduino (Arduinoâ„¢ clone) microcontroller which converts the analog signals into ADC values, and finally sends it to the smartphone using Bluetooth© wireless communication. The first phase of data gathering used signal generator and indicates the system’s accuracy and speed. The second phase testing of the study meanwhile utilizes the ECG front to get actual cardiac signals from human. This phase has already been done, though it still needs more polishing and further trials. For the final testing, nine patients of varying ages and cardiac health status will be taken with ECG readings, three replicates from the developed ECG system, and one from an actual ECG device. Using cardiologists’ and patients’ feedback, the user friendliness and accuracy of the ECG-system will be confirmed, and further modifications shall be made. Lastly, the overall cost of producing the ECG system shall be compared to the price of an ECG device, to see if the developed system is indeed cheaper. However, it is ensured that the system is far more portable than its bulkier ancestors. Once the project is fully finished, the accuracy, replicability and usefulness of the system shall be confirmed using F-test.

(一) 本研究首先導出ΔABC等分面積線移動所包絡出的曲線方程式，其圖形是由等分面積線段PQ(其中P、Q皆在ΔABC的周界上)的中點所構成，具有3 條曲線段(分別為3 條雙曲線之一部分)的封閉曲線，形成內文所謂的「包絡區」。利用包絡區的區隔，我們找出：1.當P 點在包絡區內，則有3 條等分面積線。2.當P 點在包絡區周界上，則有2 條等分面積線。3.當P 點曲線段的端點或在包絡區外，則有1 條等分面積線。(二) 以三角形的研究當基礎，擴展到凸n 邊形(不包含點對稱圖形)，我們發現：等分面積線數量之分布，仍然與包絡區息息相關，且1.凸2m +1邊形最多有2m +1條等分面積線。2.凸2m邊形，必發生內文所謂的「換軌」。因此，最多只有2m ?1條等分面積線。3.包絡曲線所分割出的區域，於相同區域其等分面積線數量相同，且相鄰兩區域數量差兩條。(三) 若凸n邊形有k個「換軌點」，則此n邊形過定點等分面積線至多有n ? k 條。(四) 若凸n 邊形為點對稱圖形(如正偶數邊形、平行四邊形)，則所有等分面積線皆過中心點。1) Our study got a curve equation of bisectors of a triangle. When a bisector is moving, we get three curves. They’re constructed by the midpoints of PQ. The three parts of the three curves make a closed curve which we called “the Envelope Area”. We found out:\r 1. When Point P is in the Envelope Area, we can get 3 bisectors. 2. When Point P is on the curves of the Envelope Area, we can get 2 bisectors. 3. When Point P is outside of the Envelope Area, we can get only 1 bisector. 2) Based on our study of triangles, we found that in Convex polygons(not including Point Symmetry Convex polygons), the distribution of bisectors is related to the Envelope Area. 1. We can get at most 2m +1 bisectors in a 2m +1 Convex polygon. 2. We can get at most 2m ?1 bisectors in a 2m Convex polygon, and the bisectors on the curves will “Change the Track”. 3. Envelope curve will divide a Convex polygon into several areas. The same area has the same numbers of bisectors, and the near areas have less or more 2 bisectors. 3) If a Convex polygon has k points to change the track, it will have at most n – k bisectors.\r 4) In a Point Symmetry Convex polygon (ex. Regular 2m convex polygons and parallelograms), all the bisectors will come through the center point.

本研究將探討所合成的金屬硫化物製備於量子點敏化太陽能電池之光電極，並應用於水裂解反應，使之產生氫氣作為新型替代能源。以硝酸鋅、硝酸鎘、氧化硒及硫化鈉作為起始物，利用化學浸泡法(Chemical Bath Deposition, CBD) 於氧化錫參雜氟之導電玻璃(fluorine-doped tin oxide, FTO)表面上，製備不同層數量子點硫化物之光電極。當CBD循環層數為1、5及7時，運用紫外光-可見光吸收光譜儀與掃描式電子顯微鏡分別可觀察到光譜變化，與球狀、團簇狀，以及緞帶狀奈米材料之結構。另外以線性掃瞄伏安法測量光電流，在一個太陽光強度(100 mW cm-2)照射下，當電壓為1.3 V (vs. Hg/Hg2Cl2) 時， TiO2/(CdZnS)4/(CdZnSe)2/ZnS光電極之光電流可達 79.24 mA，可證明經CBD循環製成之量子點電極具有高電催化活性。此外將沉積不同量子點的光電極與硫化鈷反電極結合後製成不同的太陽能電池，在一個太陽光強度照射下測量其光電轉化效率，當使用的光電極為 TiO2/(CdZnS)4/(CdZnSe)2/ZnS 時，可得最大轉化效率η為 2.40 %。更進一步，以此光電極在定電壓下進行水裂解反應，由自製的氫氣收集器收集氫氣，可得其與白金對電極產氫率為 0.98 mmol/hr，以此可確定最佳化的光電極。