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本研究以b04課程中的巴斯卡三角形為研究對象，將原先巴斯卡以「1」為首、「+」為運算符號的規律三角形，改為以「-1」及「ω 」為首、「×」為運算符號，分別就其產生的新三角形作探討，發現其中似乎隱藏著原先三角形所沒有的規律性。為了更瞭解這種規律，藉由電腦軟體繪出其圖形，圖形顯示出如碎形般的複製關係，不論放大或縮小，其中的遞迴關係並未改變，頗令人好奇，因此著手研究。研究過程中對於圖形的規律性採用先臆測、接著歸納、最後給予證明的方式呈現。得到以下的結論：一、分別以數列呈現新三角形圖形的規律性。二、分別將新三角形中每一列中的某數字（如-1、ω 或ω 2 ）的個數予以通式表之。三、分別推算出新三角形第n 列第j 行的數是「1」或「?1」及「1」或「ω 」或「ω 2 」。四、相同的模式，在特定的圖形範圍中，不斷重複出現。許多研究將巴斯卡三角形中的所有數，以某數為模的餘數紀錄下，去探討其餘數在新產生的巴斯卡三角形中的分布情形；而在碎形的研究中，大部份著重如何畫出碎形。本研究著重圖形其規律性的探討，提供上述研究不同角度的詮釋與探討。 This research subject is based on Pascal’ s triangle in senior high school curriculum. The regular triangle begins with「1」and use「+」as operation. Let 「1」 be replaced with「-1」and「ω 」, the operation sign「+」be changed into「×」. I do research on the new triangle and discover the seemingly hidden regularity which doesn’t exist in the original one. To understand more about this regularity, I draw figures through the computer. The figures show the relationship of reproduction as fractal. Whether the figure is enlarged or minimized, it’s surprising curious the recursive relationship doesn’t change, so we begin to work on research. In the process of the research, we make careful observations, assumptions and deductions about the regularity of the figure. Finally, we come to some conclusions by means of giving proofs:（1）Present the regularity of the new triangle figure with progression.（2） Present such numbers as「-1」, 「ω 」, 「ω 2 」 in each row of the new triangle with formulas separately. （3）Figure out the number in the row n and in the column j of the new triangle is「1」or「-1」,and「1」or「ω 」or「ω 2 」. （4）The same model appears again and again in the specific range of figure. Many researches record Pascal’s triangle modulo certain number to explore the distribution of remainders in the new triangle. In the research of fractal, how to draw fractal is mostly focused on. The exploration of this research emphasizes the regularity of figure, offering the interpretation and exploration of researches above from different angles.

In this research, we investigated the interactions between goldfish’ (Carassius auratus) sensory experiences (electric shock, high osmotic pressure and colors). We separated the sensory experiences into two parts. One of them, we used different kinds of environmental color-models to analyze goldfish’s environmental preference behavior and different kinds of stress experience(electric shock and high osmotic pressure) to build the animal model of environmental preference behavior. We found that goldfish prefer brown-colored environment (compared with white) and different stress has different effects on fish’s environmental preference behavior. It proves that fish has the ability to learn and memorize the stress experience and shows that there are complicated interactions among environmental stimulus, memories of stress and behaviors caused by different kinds of stress. Also, we investigated the interactions between spatial memory and color distinction. We measured the duration of goldfish getting through the color-marked barriers driven by regular electric shock. We found that goldfish spend less time to get through color-marked barriers than those unmarked. It shows that there are some interactions between spatial memory and color distinction. In conclusion, the research proves that different sensory experiences can affect goldfish’s behaviors.本實驗利用感官經驗(電擊、高滲透壓、色彩)，探討與朱文錦(Carassius auratus)行為調控的交互作用。我們將感官經驗分成兩模式：利用環境色彩特徵的差異，探討不同逆境刺激經驗(施予電擊或高滲透壓環境)，與魚類環境偏好行為的交互作用，建立朱文錦環境偏好行為之動物模式。我們發現朱文錦偏好土色環境(相對於白色環境)，而不同性質的逆境經驗，對魚類的環境偏好行為具有不同的影響，顯示魚類具有記憶逆境環境的學習能力，且證明「環境刺激—經驗(記憶)—行為表現」三者之間具複雜的交互作用。另外，我們亦探討空間記憶與色彩辨識的交互作用，利用規律的電擊刺激使朱文錦通過有色彩標示的關卡，以研究色彩差異與空間變化對朱文錦通過關卡能力的影響。我們發現色彩的標示可降低通過關卡的時間，且不同的色彩具不同程度的效果，顯示空間記憶與色彩辨識具交互作用。本實驗證明了不同的感官經驗或刺激，對朱文錦的行為調控具質與量的差異。

在網際網路蓬勃發展的時代，電腦病毒也更加的猖獗。雖說防毒軟體百家爭鳴，但對於未知病毒的防治技術仍然束手無策。本研究的目的在追溯出電腦惡意程式運行模式，利用IDA靜態反編譯軟體與病毒原始碼尋找出病毒共同的特徵，阻斷其滋生途徑。 本研究在實驗中，研究者利用Borland C++ Builder 6作為應用程式開發環境，配合WinAPI函數與TRegistry類別設計出參數監控系統。研究顯示不論是修改於Window 9x架構下的win.ini, system.ini，或是Run與Run Service之下的資料項，本系統都能有效運作。此系統能成功的攔截到惡意程式對Registry鍵值的讀寫，亦即當使用者否決其修改鍵值時，惡意程式無法在重新開機後運行；易言之，惡意程式失去執行效力。 實驗結果發現，參數監控系統可攔截惡意程式之修改命令，防止未知病毒與惡意程式開機自動運行，以此達到未知病毒的攔截基礎技術。本研究之結果可補強市售防毒系統，對於未知病毒的攔截，能達到完整的防護效果。 Computer viruses become more rampant in the rapidly-developing era of Internet. With the various kinds of Anti-Virus software, people still can do nothing about detecting the unknown viruses. This research aims to trace back the computer virus function mode. By using IDA Pro Disassembler and Virus Source, we can find out the common characteristics of viruses. Thus, we can stop viruses from thriving. The experiment uses Borland C++ Builder 6 as the Registry Detection System by coordinating Win API and TRegistry. It works no matter by modifying win.ini and system.ini under the structure of Window 9x or by modifying Run Value and RunService Value. Moreover, it can intercept the viruses from reading and writing of the ValueKey. As the users deny the modified ValueKey, the viruses cannot run after resetting. In other words, the viruses lose their effects. The results present that Registry Detection System can intercept the modifying commands and prevent the automatic running from unknown viruses. By doing so, we can acquire the basic technology of intercepting the unknown viruses. The application of this study can improve the functions of Anti-Virus. In this way, through protection from unknown viruses can be obtained.

本研究以高頻阻抗分析儀，針對自製的電容器，以不同比率的三氧化二鐵加二氧化矽混合後所製成的電容器，對頻率、電容直及正切損耗能量直從事研究。實驗結果發現，在低頻率直到60Hz以內，其 Cp及D值變化非常大，明顯的下降，60Hz到1000Hz Cp及D值變化很小。由參考資料中電容器中的損失因數是介電材料是否適合於絕緣材料用途之最基本的準則，一般均希望具有低介電率。即使在最小的空間內也希望有高電容值，如電視、收音機中在介電材料的高頻應用。是故我們所製作的電容器以二氧化矽添加三氧化二鐵後高頻值其Cp值、D值較小，是適合於高頻需求的應用上。We report on the study of high frequency dielectric spetra. On the capacitance, it is made by mnyself. At various mixed ratio value of Fe?O? pius Sio?. In order to understand the frequency capacitance value Cp and tangent loss energy analysis D. The results of our work provide a large of low frequency in o Hz TO 60 Hz in Cp and D. It is obviously descend a small various frequence is 60 Hz to 1000Hz. From reference, we know capacitance energy loss factor is a purpose of suitable an insulator rule. In dielectric constant. We hope a low dielectric value and high capacitance. Even it is a small distance. For example TV. Radio. Etc. it is used to high frequency. So we made a capacitance in difference of Fe?o? pius Sio?. To provide the Cp and D. the value is small. So it can be used in high frequence demand.

臉部皮膚會長出小小骨頭喔！皮膚多發性粟粒型骨瘤的發現，X光顯像，治病機轉與雷射在治療上的應用。本篇研究是探討一種特殊又不易偵測的骨瘤，皮膚多發性粟粒型骨瘤(MMOC)，利用各種X光顯像技術，應用在痤瘡病患，偵測其分佈、發生率和疾病之可能相關；並利用組織病理發現去推測致病機轉；且利用各種雷射光，在體內與體外進行治療性的探索，並獲致重要的結論如下：(1)MMOC非常常見，每個人都有可能發生，但臨床不易被偵測，跟性別無關，但與年齡增長成正相關；(2)病灶分佈包括額頭、眼皮、鼻子、臉頰及頸部，與痤瘡的病灶分佈十分類似，但與痤瘡的疾病活性與疤痕的嚴重度並無相關。(3)利用乳房攝影的斜切照影技術，是最簡易有效的偵測方式。(4)病理組織中有些皮膚腫瘤伴有MMOC存在，並非此腫瘤有其特異性。(5)MMOC是一個因為皮膚毛囊皮脂腺在不明顯的發炎下所造成的轉化型骨形成反應。(6)紅寶石雷射及銣-雅鉻雷射對色素性骨瘤是一有效的去除技術。鉺-亞鉻雷射及二氧化碳雷射磨皮技術，對嚴重痤瘡疤痕並有MMOC患者，亦為一良好治療方式。Multiple Miliary Osteoma Cutis(MMOC) is a kind of special condition and difficult to detect clinically. By using different kinds of X-ray techniques and compared the clinical data from the patients with acne of face, by observing the changes of skin tissue specimens for searching the possible mechanism of osteogenesis and by using scanning electron microscopic observation and energy dispersive Xray analysis for evaluating the biophysical effects on osteoma after Ruby, ND-YAG, Erbium:YAG or CO2 Laser irradiation, we concluded that: MMOC, a very common condition, may develop in everyone. MMOC can be easily demonstrated by the modified mammographic technique. The density of calcification in MMOC is not related to the sex of patients, the activity of acne, and the severity of atrophic scar but correlated with the age of the patients. MMOC, a non-specific condition, results from metaplastic ossification occurring within preexisting subclinical inflammatory processes of the pilosebaceous unit and may be found incidentally in different kinds of facial tumor. Ruby or ND-YAG laser may have some explosive effect on pigmented MMOC. CO2 or Erbium:YAG laser dermabrasion can be used to treat MMOC with acne scar.

The World Trade Center in New York City was collapsed after attacked by the terrorist. Although the design of this building did not consider the attack by the terrorist, however, this event also exposed the weakness of a high-rise building. This study is aimed at examining the cause of the collapse of the World Trade Center. A series of experimental studies was carried out to examine the strength of steel material under elevated temperature. Experimental studies were also performed on model steel frames under fire to simulate the situation of World Trade Center under fire. It is found that the strength of steel structure decayed under fire event. The upper stories lost its support from the floor that was subjected to fire load and the collapse of the floor under fire induced impact load from the upper stories. Progressive failure occurred on the subsequent floors due to the impact from the upper stories. This phenomenon was also observed in the experimental study of the model frame tests. This study has successful reproduced the failure mode of the World Trade Center in New York City. 紐約世界貿易中心大樓在遭遇恐怖份子攻擊後倒塌，雖然大樓之設計可能並未考慮恐怖份子的攻擊，但此次事件亦暴露超高層大樓的脆弱，本研究乃探討紐約世貿大樓破壞之原因，研究過程中首先以一系列之試驗探討鋼鐵材料在高溫下之行為，尤其是高溫對鋼材強度之影響。其次並進行鋼骨模型骨架受火燒之破壞試驗，發現在高溫燒烤下鋼骨軟化而失去承載能力，而無法承載上方樓層之重量，上方樓層倒塌後往下形成一衝擊力，並造成往下連續之衝擊，最後導致整體結構倒塌，模型結構試驗亦證實世貿大樓之破壞模式

隨著社會漸漸的現代化，我們需要愈來愈多的電力，然而在享用電力時，更伴隨著汗染的到來。所以討論如何有效的利用能源及探討無汗染能源，是本實驗研究的主要課題，以下即是我們的介紹。

Few plants can grow in the place where Wedelia trilobata grows. In the following experiment, the leaves ans stalks(of the plants from Wedelia trilobata) are extracted for experimental purpose .The data and records of the experiment have shown that Wedelia trilo ata indeed refain the growth of plants such as mung bean, teeding seed, yeast’s respiration and the photosynthesis. We use the function of dieing the polyphenols to know that the Wedelia trilobata can produce Allelochemicals called as the polyphemols The mesophycell produce the polyphemols from chloroplast of cortex,the polyphemols transport to root and release from root exudation. The plant will absorb polyphemols of the soil, and will affect the growth of the plant. If we can separate and purify the Allelochemicals, we can make it as natural herbicideb. 南美蟛蜞菊所在之處，少有其他植物，本實驗採南美蟛蜞菊植栽區之土壤與南美蟛蜞菊莖或葉之萃取液進行相剋作用之研究，結果顯示南美蟛蜞菊確實會抑制小麥與綠豆種子萌發及幼苗生長，並抑制酵母菌的呼吸作用及植物光合作用中之光反應。 利用多酚類染色方法得知南美蟛蜞菊產生的相剋化合物為多酚類，且該多酚類由葉肉細胞與莖內皮層中具葉綠體之細胞產生，經韌皮部輸送至根，再由根經泌濾作用釋出。土壤中的多酚類會被植物吸收，進而影響植物的生長與發育。 若能將該相剋化合物---多酚類分離與純化，或可作為具選擇性之天然除草劑。

在此研究中，我們用類似反演變換的方法，以一個定圓創立並證明了一種新的幾何變換，稱為 「調和變換」 · 我們得到點、直線、圓與圓錐曲線經過變換的關係 ·。1 .直線可以映射成原直線或一圓錐曲線 · 2.圓可以映射成一種特殊曲線。 3 .圓錐曲線可以映射成兩條圓錐曲線或一條圓錐曲線和一直線。此外我們還發現調和變換和反演變換的特殊關係 · 最後，由於調和變換可以簡化圓錐曲線的關係，我們將調和變換應用在行星輾些的證明上，並得到了良好的結果。In this research, we use a method similar to the inversion to establish a new geometric transformation, called harmonic transformation, by a fixed circle O, we prove some of its properties. We have gotten the relationship among points. lines, circs, conies and their images: 1 .The image of a line is a conic or a line itself. 2.Thc image of a circle is a special category of curve. 3.The image of a conic with its focus at the center of O is two conies or a line and a conic. Further mote, we also find the special connection between harmonic transformation and inversion. Finally, since the harmonic transformation can simplify the conic, we apply the harmonic transformation to identify the orbit of a planet, and obtain a nice conclusion.

本研究是藉由數學手法探討；如何由一疊36 張四種花色的撲克牌中，尋找出保證可猜中最多張花色的方法。研究過程是以在適當的猜牌時機，以鴿籠原理、邏輯推理、二進位、分析與歸納……等數學原理與方法，搭配巧妙的策略運用而達到目的。猜牌方法：先約定好猜牌規則，助手將36 張牌背圖樣相同但非對稱的撲克牌，以旋轉牌背的方向傳達訊息。在本研究中得出利用數學原理與方法可「經由巧妙的猜牌方法保證可以猜中26 張花色」，並提供後續研究者利用本研究之結果繼續深入探討與研究。 The study is mathematically based with reasonable explanations behind it. We are to correctly guess as many cards as possible from a deck of 36 cards, with random numbers and four different suits. We will apply mathematical methods, such as pigeonhole principle, logic inference, binary system, and analytical reduction, upon right timing. Using careful arrangement of the principles and reasoning, we can reach our ultimate goal. To state guessing: Conference between the guesser and the assistant about the guessing rules, the assistant will have 36 cards with the same exact pattern on the back but not symmetrical. The pattern of the cards will be different when rotated 180o. The only communication between the two is by rotating cards. In the process we will obtain mathematical theory and methods assuring 26 cards correctly guessed, and the study is for further and deeper discussion.