未得獎作品

地震波會以橫波和縱波的方式傳遞能量，學校的教學大樓中地下具有蓄水池者搖晃的持續性感覺比較短暫，於是利用彈簧波模擬地震波測試不同質量的台車接收到的能量會較空車為多。並利用自製模型測試不同容器形狀和水量的阻尼作用，結果發現搖擺時，時間球形＞錐形台≒方形台；球形台裝有不同水量時擺動時間裝滿裝滿時＞未裝水＞裝1500mL 時；平行移動時則是球形台裝水2000mL 後鉛錘移動距離最短。整個實驗過程中由於未裝滿水的模型內部重心改變不規律，而且模型內所裝的水量因為不規則擾動經吸收的能量轉換成水溫上升的熱能，因此導致擺動能量的消耗造成擺動時間縮短，如果新式大樓興建時考慮消防蓄水池和水塔的造型和裝水容量，應可以減少地震時的搖晃時間，降低心理的緊張和物體因震動而產生的移動傷害。Seismic wave can transmit energy with transverse and longitudinal wave. The shaking of these buildings with reservoirs underground in our school for a shorter time, so we use spring wave to simulate seismic wave, and test the proportion of transmissible energy received from different mass of objects. The energy gets from wave motion passing on is bigger when cars carrying capacity than empty cars. And we use homemade models to test damped effect of different forms and water. At last we discover the time is Sphere ＞ Taper ≒ Square while they swing with different amounts of water, the time it cost is Full ＞ Non ＞ 1500 mL. When they move horizontally, the plummet moved shortest, when the water of the sphere is 2000 mL. During the whole experiment, the center of gravity in the models, which are not full of water changes irregularly, and the water in the models can absorb heat energy from energy disturbing, so the swing of energy consuming makes the time of the swing shorter. If the fire controls reservoirs, the shapes and dress up water volume of the water towers, are taken into consideration, the duration of the shaking of earthquake will be shortened so that our fear and nervousness will be lessened, and the damage causer from the shaking will be reduced.

This research primarily aims to observe how does the electric work, why does it work and the relationship between the surrounding circumstance and the repulsive torque. The electric whirl is made of an enameled wire bent into right angle with sharpened ends. When an AC high voltage is applied, the electric field intensity around the whirl ends is strong due to the small curvature radius of the ends. The molecules in air at both ends are ionized. This cause the phenomenon of point discharge. The positive and negative ions produced by alternating current forms AC ion wind, and produce a torque to make the whirl rotate. The object of this experiment is to observe the relationship between the surrounding circumstance and the torque repulsion. We design an apparatus to measure the angular velocity of the rotating whirl. We also calculated the kinetic energy of the whirl and the work done by the torque. The repulsive torque can be obtained by Work energy theorem. Result: (1)The angular velocity of the electric whirl is direct ratio to repulsive torque. When we want to find out the relationship between the manipulate reason and the repulsive torque, we can just compare the angular velocity with the manipulate reason. (2)The angular velocity of the electric whirl is only related to the peak voltage, and it does not make difference whether we apply AC high voltage and DC high voltage. (3)When the humidity is over 68%, the electric whirl cannot function normally. (4)Under the low-pressure circumstance, the electric whirl will rotate with glow discharge and the angular velocity will decrease to zero gradually.本實驗是探討電離轉輪的性質、原理與周圍環境的關係。「電離轉輪」為漆包線兩端折成直角並磨尖而成，接上交流高壓電源時，其尖端曲率半徑小，電場強度相對大，會游離尖端附近的空氣分子，產生尖端放電的現象，而交流電交替產生的正、負離子會形成交流離子風，並產生轉動力矩，使轉輪轉動。我們設計一個裝置，使其能偵測轉輪轉動的狀況，運用測得數據計算出轉動時的動能和作功狀況，套用功能定理便可求得轉輪通電時產生的斥力矩。實驗結果顯示(1)轉輪的角速度和尖端斥力矩成正相關，所以當我們想得知尖端斥力矩和實驗操縱變因的關係時，只要比較角速度和操縱變因就可以了，這簡化了原本繁複的計算和冗長的數據處理過程。(2)轉輪的角速度只和峰值電壓有關，和直流或交流沒有直接關係。(3)轉輪在超過溼度68%之後，就不會正常運作。(4)在低壓條件下，轉輪轉動時會伴隨淡紫色的輝光放電(glow discharge)現象，而抽氣塔中與轉輪尖端最接近的一點，也就是電場最強的一點，會和尖端同時產生光芒，相互輝映。

流行病的傳染如同一個無尺度網路，但有一些特殊特性在發展一套新傳播模式時，是需要被詳加考慮的。我採用時間位移(t 與ti 分別以t?(ti?1)與ti?(ti?1)來取代)至無尺度網路模式中，再引入一個非連續強力函數H(t; ti?1, L+ti?1)來描述流行病傳播的特定時段與強度，並重新定義機率p 為無效傳染率。之後，我建立了新模式「無尺度流行病模式」－SFE-1與SFE-2。模擬六種病原的傳染途徑，結果證實SFE-1與SFE-2模式是正確與確切可用。案例研究結果，顯示傳染強度H可為固定值或為變數；p可以是一固定值、雙固定值或為新增病例的函數。更進一步解析美國AIDS病例在不同族群與行為上的差異，獲知亞裔/太平洋裔與印第安人/阿拉斯加人的H值低於其他族群，其原因可能是由於小的族群具有較高的接觸所致。異性性接觸的H值低於其他，顯示性交易是傳播HIV的主要途徑。SFE-1與SFE-2模式也可被用在流行病的預測上，因為SFE-2使用已知值而非估算值，所以SFE-2模擬結果較佳；但是SFE-1更可以明確提供一個流行病在失控或控制下的預測結果。無尺度流行病模式可以協助所需警戒的程度與政策決定的計畫結果。因此在幫助政府評估社會經濟成本與健康憂慮上是一個有用的工具。所以我提出一個確切可行的對抗無尺度流行病傳染新方法，並詳細說明運作流程。The course of epidemics resembles a scale-free network, but some specific elements should be considered in developing a new model. I introduced a time shifting (replacing t and ti by t?(ti?1) and ti?(ti?1)) and a discontinuous forcing function H(t; ti?1, L+ti?1) into the scale-free network model to fit the specific period and intensity of the infection, and redefined the probability p as an invalid infection rate. Then I proposed the new Scale-Free Epidemic Models, SFE-1 and SFE-2. The simulation results of six types of epidemic transmission showed that the SFE models were accurate and useful. In the case studies, the results showed that H were constant or variable, and p were a fixed constant, a dual constant, or a function of new addition cases in the epidemic periods. The further studies for comparisons of the difference races/ethnics and the difference transmission category of AIDS cases in USA were analyzed. The H value for Asian/Pacific and Indian/Alaska Native race were lower than others, it may be due to small clusters with constant high contact rates. The H value for heterosexual contact was lower than the others, indicating that whoredom was the main transmission for HIV. Both SFE models can be used to predict epidemics, SFE-2 is better than SFE-1 due to SFE-2 using given indices and not conjectured values, but SFE-1 can more clearly suggest results of epidemics when under control or not. SFE models can help the government to determine the level of caution needed and the projected results of policy decisions. They are useful tools in assisting to balance socio-economic and health concerns. I hereby propose a new method to fight against epidemics with detailed procedures of using the SFE models.

這個題目是源自2003年的TRML思考賽的題目，原題目並不難，它只有用到簡單的排列方法，主要是討論 an 、bn 兩種數字的排列，其中 an 為滿足下列所有條件之N位數A的個數。 I. A中每一個數字為1或2 II. A中至少有相鄰的兩數字是1 而 bn 表示滿足下列所有條件的N位數B的個數 I. B中每一個數字為0或1 II. B中至少有相鄰的兩數字是1 以及探討an 、bn 與費氏數列cn之關係，其中 cn = cn-1 + cn-2 ，n≧3 ,c1=1, c2=2 。 其中 an 如果改成考慮為一數列，其值不變；而 bn 如果改為數列，那麼就不需要考慮0不能為首位數字的情況。如此，讓人聯想到一個用生成函數解的題目「一個N項數列，其中每一項只能是0或1或2，其中0和2永不能相鄰，求這個數列個數的一般式。」，因此，我們嘗試將這個題目改變它的要求繼續做下去，發現其中有某些規則，例如：不只是原來的11相鄰，甚至是排列其它種方式，都可能從其遞迴式看出它排列的意義，甚至這種排列數是可以用遞迴式求出來的。這提供了我們另一種求數字排列的方法，也是我們覺得有趣的地方。 在過程中我們初步得到以下結論： This solution is according to power contest of 2003 TRML. It is composed of two number arrangements, an , bn . First, suppose an is the total number conforming to the following rules. I. Each number is 1 or 2 in A. II. There is a couple of (11) in A at least. Then, suppose bn is the total number conforming to the following conditions. I. Each number is 0 or 1 in B. II. There is a couple of (11) in B at least. Furthermore , we give the thought to the relation among an ， bn ，and cn (Fibonacci Sequence). By the way, if an is changed to a sequence, and the result is the same. But if bn is to arrange number, we have to give thought to the fact that the first number can’t be zero. If it is a sequence, we don’t have to consider it. The problem belongs to combinatorics. After we do this problem, we find not only original question but also other permutation can be understood by its formula. The problem provides us with other means to solve permutation and combination question. Then, we get the conclusion as follows：

一、若Mn×n(s)表示在n×n 的正方形棋盤中，排列s 顆棋子在方格內，且每一方格最多只能排1子，其中s 顆棋子的配置需滿足兩個條件：1. 並無任意4 子可以形成矩形框的4 個頂點。（此矩形框的邊需與棋盤的邊平行）2. 在沒有棋子的方格中，無法再加入棋子。二、若Vn×n×n(a1,……,an) 表示在n×n×n 的正方體棋盤中，每層的棋子個數分別為a1,……,an，且s= a1+……+an，其中s 顆棋子的配置需滿足兩個條件：1. 並無任意8 子可以形成長方體的8 個頂點。（此長方體的邊需與立體棋盤的邊平行）2. 在沒有棋子的方格中，無法再加入棋子。本研究即在Mn×n(s)與Vn×n×n(a1,……,an) , s= a1+……+an 中探討s 的最小值、最大值及變化情形，並分析其配置方法。之後推廣至長方形Mn×m(s)及長方體Vn×m×k(a1,……,ak) , s= a1+……+ak。最後根據其研究結果設計一個「避開矩形框棋」，並加以分析出致勝的策略。一．If Mn×n(s) indicates in the n×n square chessboard, we put s chesses to line in the square and each square only can put one chess. Then the station of s chesses must satisfy the following two conditions：1. No any 4 chesses can form the tops of the rectangular frame ( The sides of rectangular frame must be parallel to the sides of chessboard )2. If there’s no chess in the square, we can’t add any chess. 二．If Mn×n×n(a1,……,an) indicates in the n×n×n square chessboard, the chess number in each layer are a1,……,an and s= a1+……+an. The station of s chesses must satisfy the following two conditions： 1. No any 8 chesses can form eight tops of the rectangular cube ( The sides of rectangular cube must be parallel to the sides of cubic chessboard ) 2. If there’s no chess in the square, we can’t add any chess. This research try to explore the minimum, maximum and variation of s which in Mn×n(s) and Mn×n×n(a1,……,an), s= a1+……+an, and analyze its station. Then we will extend the research to rectangle Mn×m(s) and rectangular cube Vn×m×k(a1,……,ak), s= a1+……+ak. Finally, according to the result of research we wish can design one “avert rectangular frame chess“ and analyze the strategies to triumph.

本研究主要探討蝌蚪之游泳運動特性，及游泳速度(V)與尾鰭長度(SL)、尾鰭高度(SH)、身體質量(M)、尾鰭擺動頻率(TBF)、擺動幅度(AMP)之關係，並分析蝌蚪游泳之體軸變化及流場變化。祈能了解蝌蚪之游泳運動特性，進而探討其適應環境之機制。研究結果顯示：黑眶蟾蜍蝌蚪體重(M)愈重，則鰭長、鰭高亦隨之生長，並呈現高度相關性(R2=0.9381、R2=0.9809)。另外，尾鰭生長時之長度增加較多。蝌蚪體重(M)與鰭長(SL)、鰭高(SH)之迴歸方程式(M=0.027SL＋0.342SH－0.078，R2＝0.9832)。黑眶蟾蜍蝌蚪之游泳速度，會隨著尾鰭擺動頻率之增加而提高。尾鰭長度愈短之蝌蚪，增加游泳速度時尾鰭擺動頻率增加較多。蝌蚪游泳速度(V)與鰭長(SL)、擺動頻率(TBF)之迴歸方程式(V=0.480TBF＋4.804SL－4.381，R2＝0.9110)。不同尾鰭長度蝌蚪之擺幅對體長之比率並無明顯變化，其擺動幅度(AMP)的範圍介於0.45(BL)至0.56(BL)之間。蝌蚪游泳時各部分體軸之擺動幅度自吻端開始(P=0)至P 為0.24 時逐漸遞減，且在P 為0.24 時呈現最小擺幅，但P 超過0.24 之後直至尾鰭部分卻又大幅遞增，其最大值出現在尾鰭末端(P=1)。蝌蚪游泳是以尾鰭快速向中心軸擺動，產生較大的前進動力，過了軸線則慢速擺動，以減少阻力。This investigation is to explore the swimming habits of tadpoles- the relationship between their swimming velocity, length and height of their tails, mass, the frequency at which their tails movement, and the amplitude of the tail’s movement, as well as analysis their body axes, and the flow distribution of the water, in order to understand how the swimming patterns of the tadpoles are affected by the changes in their environment. The results of this investigation have shown that as the mass of the tadpoles increases, both the length and the height of their tails also increase according to the R values of the tail increases according to the R values of 0.9381 and 0.9809. However, it is observed the length of the tail increases at a faster rate than its height during the tadpoles’s growth. The formula which models the regression relationship between the tadpole’s mass, tail length, and tail height are found to be (M=0.027SL+0.342SH-0.078,R=0.9832). It’s also noted that as the length of the tadpole’s tail decreases, the velocity and the frequency of the tail would increases (the length of the tail is inversely proportional to the tadpole’s velocity and tail frequency). The formula which models the regression relationship between the tadpole’s velocity, tail length and tail frequency is (V=0.480TBF+4.804SL-4.381,R=0.9110) The different frequency model by tails of different lengths do not appear to have an apparent relationship with the tail length, given that the amplitude is between 0.45(BL) and 0.56(BL). As the tadpole swims, the angle between its oscillating body axes decrease as the P values increases from 0 to 0.24, their force the angle is at a minimum whom the P is at 0.24.Yet when P exceeds 0.24 the angle would increase dramatically. The maximum value is observed when P=1.The tadpole’s swimming motion mainly relays on the rapid oscillations of the tail about the centre of mass (body axis)-producing a stronger driving force, and slowing down towards the end of each oscillation to minimise the friction forces acting on the tadpole, which in furn, decrease its velocity.

本研究由下述問題開始：將n1 個黑色棋子和n2 個白色棋子排成一列，規定第一個棋子必為黑棋；對於每一種排列方法中，同色棋相鄰處記為1，異色棋相鄰處記為-1，所有1 和-1 的總和記為 t (n1,n2 )。對所有可能的排列方法所算出來的t( n1,n2 ) 值求其平均值，記為a (n1,n2 ) 。我們先由觀察各種n1 和n2 值，得到這平均值的可能公式，隨後並嚴格證明其正確性，證明方法也經過多次精鍊到十分簡潔的方式。以此為基礎，我們並做了各方向的推廣，研究涉及下列各點：(一) 利用組合數探討原來的問題。(二) 在第一個棋子不限定為黑棋的假設下，求平均值a( n1,n2 ) 。(三) 將棋子由兩種增加到多種。(四) 改變棋子排列以及相鄰的方式。經由研究，我們發現，每一次愈將問題推廣時，愈能找出清晰的概念涵蓋並印證先前的想法。Our study starts with the following problem. Suppose n1 black chesses and n2 white chesses are arranged in a line under the condition that the first chess is black. For any arrangement of these chesses, an adjacent pair of chesses having the same (respectively, different) colors is associated with a value of 1 (respectively, -1). Let t(n1,n2 ) denote the sum of these values. The purpose of this problem is to calculate the average value a (n1,n2 ) of these t (n1,n2 )which runs over all possible arrangements of the chesses described above. We begin from observing various values of n1 and n2 and find a possible formula for the solution. We then give a rigorous proof for the formula. After some refinements, simple proofs are also established. Based on this, we also make some generalizations. In summary, the research includes the following: 1. Study the problem by using binomial coefficients. 2. Calculate a(n1,n2 ) when t( n1,n2 ) runs over all possible arrangements in which the first chess can be black or white. 3. Increase the types of chesses from two to many. 4. Variant the arrangement method of the chesses from a line to other configurations. During the study, we find that whenever we extend the problem to a more general case, we make the ideas for the original problem clearer.

本實驗係以台灣常見之數種植物(甘蔗、橡膠、破布子、苦苓)乾餾所成之多孔性碳棒鍍上銅和拷上Chitin 為電極兼電容，而以NaOH(aq)為電解液，製成化學電池。希望能研究出一低污染、低成本、能在常溫下經濟運作、並具有教學演示功能之電池。This research is based on the poromeric carbons which are made of several Taiwanese common plants (including: sugarcane, babul, Sabastan Plum Cordia [Cordia dichotoma Forst] , and Chinaberry tree [Melia azedadach L.]) by means of destructive distillation. The copperplating poromeric carbons later covered with Chitin functions as an electrode ac well as capacitance. Along with NaOH(aq) eletrolyte, a accumulator is then produced. The chief objective of this research is to produce a accumulator with low class of pollution and low cost, which is able to function economically under the normal atmospheric temperature. Also,this accumulator can serve as a teaching demonstration.

在高中光學裡，介紹了許多有關光波之特性，而聲波與光波皆具有波動性，因此聲波應具有如干涉、反射、聚焦等特性，但在物理課本上並未詳加敘述，所以我們開始了本項的研究，希望可以籍由改變聲源及邊界的各項條件，而探討其發生之現象。在本研究中，我們利用聲波之基本原理在電腦上進行聲場的模擬並加以改變其變因（頻率、相位、聲源數、聲源間距、強度、邊界反射），進而明瞭聲場之各項特性及應用與控制方式。經電腦模擬聲場圖中，我們觀察到，兩聲源干涉所形成之圖形為多組雙曲線所組成，近似於光學之雙狹縫干涉，增加聲音頻率與聲源間距離皆可使腹(節)線數目增加。如同現實世界中所知的，隨著頻率的增加，將會具有指向性的產生並且在聲源數目越多時越明顯，但發現頻率增加至一定值之後，指向性反而會降低而形成冠狀面。在延遲了多點聲源間相位之後，聲場分佈有偏轉之現象，利用相位延遲的方法，在多聲源中，將兩旁之聲音偏向中央將可造成聲音的聚焦。在兩聲源干涉中，調整其中一聲源之強度，將可完全消除兩音源連線間一點之聲音，可適當的應用在工業上消除噪音。聲場分佈在具有邊界的環境下，我們試著找出聲源位置及邊界條件對聲場分佈的影響與關係以模擬室內聲場，但在簡化的數學模式下，即無法有我們所希望之最均勻聲場分佈產生。最後我們將實驗中的結果與文獻上的實驗數據加以比較，以探討其誤差。 The optical course in senior high school , which introduced many characteristics of optical wave. However, both of sound and light have the characters of wave; therefore, sound wave should have the characteristics, such as interference, reflection and focalizing. Nevertheless, there are not many details of sound wave in the section of acoustic on our textbook. So we began this research, and discuss the different phenomena by changing many kinds of variables. In our research, we simulated the sound field on the computer, based on sound wave’s principle, furthermore we change many variables, which like frequency, phase, source number, distance, intensity and reflection. It helps us understand the characteristics of\r sound, how to control sound and how to apply these findings. According to the result of computer simulation, we discovered that the graph of two acoustic source’s interference comprised by many pairs of hyperbola, just like optical double slit interference. As the frequency or the sound source distance increased, acoustic direction became more and more obvious. But when the frequency was high enough to over the extreme, instead increasing, the acoustic direction would lower down like a crown. After we make phase differences on one of the two sound sources, sound field generated\r deviation. So if we use this method in multiple sound source, and delay the middle source, the sound field might be converged. In such two-sound-source interference pattern, when we control the intensity of one, a certainly point on the line of the two sources disappeared When the sound field enclose by borderline, the standing wave appear, and we discovered many funny phenomena. We put large amount of source in a narrow slit, the phenomenon of diffraction appeared. Finally, we discussed the discrepancies between interference pattern previously done by others experiments and the simulated one conducted by us.

利用陰極電弧蒸鍍各種薄膜，如：類鑽膜（DLC）、氮化鈦膜（TiN）、氮化鉻膜（CrN）、氮化鋁鈦膜（TiAlN）以及先披覆上一層氮化鋁鈦膜（TiAlN）再加上類鑽膜（DLC）的合成膜等。這些薄膜現在已經被廣泛的應用於各種刀具、模具的表面處理之中。本研究主要在探討高速鋼鍍上氮化鉻膜（CrN）之後，對於硬度、磨耗性質的改變，以及觀察氮化鉻膜（CrN）表面結構之組織。 在研究中我們運用陰極電弧蒸鍍系統蒸鍍氮化鉻薄膜，分析上運用SEM來觀察薄膜表面結構組織，以及運用洛氏微硬度機來觀察試片的硬度，另外還有使用磨耗試驗機來進行磨耗測試。以上這些測試總括來說都是在得知性質有無實際上的改變，而這些實際上的改變對於蒸鍍之後的模具或刀具都能夠大幅的提高使用的壽命。 We evaporated different kinds of thin films by using the anode of the electronic arc, such as DLC (Diamond-Like Carbon), TiN (Titanium Nitride), CrN (Chromium Nitride), TiAlN (Titanium Aluminum Nitride), and synthetic films of covering TiAlN and DLC. These thin films have been used widely in processing the surface of a variety of cutters and moulds. The purposes of this research were to investigate changes of hardness and abrasion and to observe the organization of the surface structure of CrN after High-speed steel evaporates CrN. In this study, we use the system of the anode of electronic arc to evaporate CrN. Besides, SEM is used to observe the organization of the surface structure of the thin films and Rockwell Micro-hardness Test Machine is used to investigate hardness of testing samples. Moreover, we use Abrasion Tester to test abrasion. These tests are taken to lead to a better understanding whether the quality really changed. These changes of evaporated moulds or cutters would extend their frequency of using.