2004年

本研究中，我們將提出一些新穎結果，著重討論其在三角中的應用；同時，找出其遞迴關係式，得出三角展開式與其所對應之多項式分解式，進而討論出多種的規律性及所涵蓋的內容及推廣性質，我得到很多高中數學公式無法推導出在【4】和【8】中的漂亮公式及創新的結果，且這些等式都是由我們不太瞭解的無理數所構成的。 主要是討論我們在【7】中所得到的收穫與經驗；複數是三角、幾何、代數互動的橋樑，我是以不同的角度及嶄新的方法來綜合探討在【6】中相關的應用。提出關於正整數平方的倒數和公式更為精簡且基本的證明，將 sin−2 x 表示成級數形式的部分分式，進而應用在(a,b) = 1的機率問題上；並研究相關的等式，直接透過三角與代數來研究關於 2p 次方的倒數之求和問題，得出級數 之和的有用遞迴公式，並與最重要的常數扯上關係。 For one thing, we present diverse methods to evaluate finite trigonometric summation and related sums. Trigonometric summations over the angles equally divided on the upper half plane are investigated systematically. Several related trigonometric identities are also exhibited. What is more, we use methods of calculus, and make several surprising and unexpected transformations. A useful recursive formula for obtaining the infinite sums of even order harmonic series, infinite sums of a few even order harmonic series, which are calculated using the recursive formulas, are tabulated for easy references. Furthermore, is there any interesting results and applications？ Finally, the purpose of this paper is to develop a new proof of and related identities, but their derivations are more complicated. The following studies are completed under the instruction of the professor.

Generally speaking in order for a exotic plant life to dominate over the local ecology, the following factors must hold true: 1. A close proximity of the environment (including geographical and climatic factors) 2. A lack of nature enemy and competitor 3. A strong reproductive and adaptability capacity. Base on the above factors, We will be using Field Observation record, Sample placement, virtual environment factor experiment and other methods to conducing our investigation. This study shown the African Touch-Me-Not（Impatiens wallerana） has a strong reproductive and adaptability capacity. Even under adverse condition the African Touch-Me-Not survive for a period of time. It can produce flowers then fruits all year round, within each fruit there is on average 45 seeds with, under the right condition, near 100% germination rate. It can also reproduce asexually via cutting. Taiwan’s warm and humid geographical condition is similar to its origin of Africa. And so far haven’t found any obvious natural enemy. In the future this plant will be likely to spread on the low to mid. level mountain region. It also can be seen that the divergence within its habitat is low. Therefore it will decrease the variety, the density and the diversification of the local eco-system. Here to advise the government’s forestry and agriculture department, to study the relevant ecological information on this species, when they are considering popularization this plant. Using the information to evaluate the impact of this plant may have on the environment, and use it as a guideline for their plant conservation policy. 一般而言，外來植物入侵本地原生植群成功的條件有：一、相似的環境（包括地理、氣候等因素）。二、缺乏天敵及競爭對手。三、旺盛的繁殖力和適應力。針對上述條件，利用野外觀察記錄、樣區設置及模擬環境因子實驗等方法，來探討非洲大鳳仙未來是否會在臺灣蔓延、擴展進而影響本土的生態系。結果顯示非洲大鳳仙有旺盛的繁殖力和適應力，?使在不利的環境下，短時間不會死亡。一年四季皆可開花結果，每粒果實平均有四十五粒種子。環境適宜時，有接近百分之百的萌發率，亦可用莖進行無性繁殖。另外，臺灣溫暖多雨的地理環境亦與其原產地非洲相似，且未發現明顯天敵，未來極有可能在中低海拔山區蔓延。調查也發現它生長的地區岐異度明顯偏低，使其他植物種類、密度減少，生物多樣性降低。因此建議政府、森林、園藝和農業工作人員在推廣時，多吸取相關物種的生態學資訊，評估其對環境可能造成之影響，以作為植物保育之重要參考。

Tea is the most widely accepted and consumed beverage worldwide due to its characteristic aroma and taste. Recent studies have provided the strong scientific basis for understanding the health promoting effects and cancer preventive actions of tea. The components of tea especial the catechins are varied with the conditions of making tea. To understand and determine the chemical composition of tea is very important. Some investigations of the parameters on the storage and making of tea were carried on in this study. The kinds of tea studied were including black tea, oolong tea, green tea, and instant tea bags. A high performance liquid chromatograph combined with UV detector and mass spectrometer used to analyze the components of tea. The results showed that the composition of tea solution is dependant of the exposure of light. One of the components of tea, (-)-epicatechin methylgallate (ECMG) was oxidized to quino form. The concentrations of (-)-catechin gallate (ECG) decreased and one of new compound (M.W. 442) produced with increasing the storage time. From the results show tea made with cold water is better than that made with hot water. The ingredients in green tea were changed faster than those in fermentative black tea and oolong tea. The components of tea can be kept unchanged for a long time at low temperature. In refrigerator, the time can be extended to overnight. 茶由於其具有特殊的芳香氣味及口味，廣泛地被世人用為飲料，近年來的研究證據顯示茶具有促進身體健康和防癌功效，但茶中成分之變化，尤其兒茶素隨茶的種類、茶沖泡保存方式及置放時間而有所不同，因此對於茶中成分及沖泡方式的認知是一門重要的課題。 本實驗主要是探討茶沖泡時間及貯存條件，對於茶液所含兒茶素變化的影響，探討的茶包含紅茶、烏龍茶、綠茶及其茶包。並使用質譜儀及高效能液相層析質譜儀配備紫外光偵測器分析茶液中之成分，實驗結果顯示成分變化速率以未發酵的綠茶較發酵的紅茶和烏龍茶快；低溫儲存時，亦可延緩茶液成分的變化，例如加蓋並存放於冰箱，則茶置放至隔夜其成分均未改變；同時結果顯示成分產生變化者，主要為兒茶素氧化，如將多酚類氫氧基經氧化變成?（quino） ，其次為斷裂再產生聚合其中綠茶以不照光變化較大。本研究並經實驗發現如果以冷開水沖泡綠茶20~30分鐘，咖啡因的溶出量雖略多於沖泡2分鐘的熱茶，但各種兒茶素的溶出量卻遠高之，尤其置放至隔夜茶液成分仍無氧化現象。

Hamiltonian和Hiroimono路徑問題都有百年以上的歷史，且沒有直接解決方法，可能因為是題目本身的條件在討論時尚不足解決問題，現階段只能用電腦去跑。

本實驗是控制奈米碳管的成長條件，研究奈米碳管的成長機制、電子場發射特性。奈米碳管的物理性質會因捲曲度(helicity)、管壁厚度(單層或多層)、管徑所影響，而不同的捲曲度，會形成不同電性(金屬性或半導體性)的奈米碳管。由此可知，探討奈米碳管的成長機制，以控制奈米碳管的穩定成長，及如何長出電性或光學性質相近的奈米碳管，是極為重要之事。為了研究奈米碳管的成長機制，我們使用微波電漿輔助化學氣相沈積法 (Microwave plasma ehanced chemical vapor deposition) ，在市售的縫衣針針尖上，成長奈米碳管，這個技術能夠經由吸收微波達到局部加熱針尖的方式，再透過控制微波功率、通入氣體的種類、壓力的變化以及催化劑的使用，能夠達到有效控制奈米碳管的成長條件。我們改變三個參數：催化劑的使用、氣體種類(Ar+CH4 或N2+CH4)及壓力，之後利用SEM 觀察奈米碳管的成長情形；再測量場發射(測量電性)，討論不同成長的條件與場發射電流關係。

本實驗利用「閃光攝影術」，由拍攝桌球碰撞球拍拍面瞬間照片，希望能測量桌球與拍面的接觸時距、摩擦力、恢復係數。近年來，數位相機已經具有單眼相機所有功能，所有攝影參數可記錄調整，並且可以馬上看，作影像處理，大幅降低拍攝費用，若配合高速閃光燈，可以拍到重複曝光照片，所有的數據由照片測量，是計算碰撞問題的新的構想，適用於所有球類的碰撞。

在「植物的秘密生命」這本書中提到植物在電場或磁場中會生長的更好，我最近正好學到了電磁場如何產生，以及一些產生電磁場的方法，所以本研究即利用螺形管線圈來產生均勻的電磁場，並用運用安培右手定則來控制磁場產生的方向，來探討電磁場在不同條件下對實驗植物－綠豆生長的影響。本實驗使用銅質線圈纏繞鐵碗的方式，且通入不同大小電流來改變磁場的強度，以探討對實驗植物－綠豆生長的影響。本研究所得到的結果顯示：(1)綠豆在通入電流50mA 時所產生的電磁場可促使綠豆達到最好的生長效果；(2)栽培綠豆環境中所架設的電磁場較高，可使綠豆表現出較為明顯的生長速率；(3)促進綠豆的生長並不需要二十四小時都通入電流；(4)綠豆在N 極朝上的電磁場中生長的速率較S 極朝上的磁場中要快；(5)在較低溫度環境中，電磁場促進綠豆生長的效應較為顯著。;It has been mentioned that the plants will grow faster in the electronic or magnetic field in the book of “the secret life of plants”, I learned about the knowledge and methods of how to produce the electromagnetic field just now, I use the screw wire to produce electromagnetic field and control the direction by the Amplifier’s rule to investigate the growing speed of green beans under electromagnetic field in those different temperature. In this experiment, I use the wire to screwed around the ironed bowl, and make different electric current to generate different strength of electromagnetic field, the results indicate that (1) The faster growing speed will only exist in some strength of electromagnetic field, (2) The higher ironed bowls that full of screwed wire will result in the faster growing speed, (3) It will not need electromagnetic field all days, (4) The green beans will grow fast in those north magnetic pole than those in south magnetic pole, (5)The effect of electromagnetic field to increase growing speed will be significant in higher room temperature.

如果n-1 個正四面體在n 個面的多面體棋盤中翻轉(如：正八面體、正二十面體、五邊雙菱錐及三角錐台棋盤)，則正四面體相互之間會受到很多限制。本研究為探討n-1 個正四面體在n 個面的多面體棋盤中，利用其翻轉的特性，翻轉至相鄰空格，進而完成：1. 每個正四面體的底面及側面均能「同色共面」。2. 在滿足以上的兩個條件下做「數字排序」。3. 探討每個遊戲在各階段是否有解的情形。最後，將遊戲推廣至正八面體在多面體棋盤中的翻轉。If n-1 pyramids can turn in the chessboard of n planes pyramids (ex: 8 planes pyramid, 20 planes pyramid, 5 sides bi rhombus pyramid and triangular pyramid chessboard) there are lost of restrictions between these pyramids. This research is discussing about the n-1 pyramids in the chessboard of n planes multi pyramid, which have the peculiarity of turn that can turn to nearby space. We found that: 1. Each pyramid’s button plane and aide plane can be “same plane same color”. 2. Matching about 2 conditions then can do “order by numbers”. 3. Search for answers of each levels in each game. Finally, the game will be propagated to eight planes pyramid can turn on the chessboard of multi pyramid.

One of the anthropogenic influences on the permafrost landscapes is deforestation and breach of the surface cover at the road constructions. On these areas a development of various cryogenic and postcryogenic processes and features (thermosubsidence, knobs (bilars, baydjarakhs), ravines, small lakes - djyodje) is being observed. Such features can be observed on the territory of Megino- Kangalassky Region, which is situated in the Central Yakutia, as well. During the period from 1998 to 2003 the author carried out monitoring studies of cryogenic features along three roads. Ten areas measuring twenty square metres were put in all. During 6 years of research about 1520 measurements of cryogenic formations parameters were made. Based on the results, it is concluded that elimination of the shadowing effect by trees and removal of the surface cover along the roads have caused thawing of shallow-lying ice wedges, as well as development of various cryogenic processes and features. In this paper, the author presents the basic technologies which are used in road construction in permafrost areas and, based on the research results, proposes a set of measures for rehabilitation of the roadside areas.

動脈硬化是個致病率和致死率相當高的慢性發炎疾病，為台灣十大死因之一。在病理過程中血中濃度過高的膽固醇為動脈硬化的一大危險因子，其會誘發一連串的發炎反應驅使血管壁內皮細胞功能喪失，血壓上升，平滑肌細胞增生等。Statin 是臨床上十分有效的降血脂藥物，雖然其作用機制已知在於抑制膽固醇合成酵素 HMG-CoA reductase 而有降血脂功效，但近年來探討 statin 在抗發炎方面的作用也漸受重視。nitric oxide synthase (NOS) 代謝產物如 nitric oxide (NO)，cyclooxygenase (COX) 代謝產物如 prostaglandin (PGE?、PGI?)，及 heme oxygenase-1 (HO-1) 代謝產物如 carbon monoxide (CO)，均有文獻指出可以改善血流，而可能在動脈硬化上扮演保護角色。相反的，matrix metalloproteinase (MMP) 的表現會誘使更多的免疫細胞浸潤到血管壁，並增加動脈硬化斑破裂，引起栓塞和中風的發生。在此實驗中，我們利用培養的大鼠主動脈血管平滑肌細胞作為研究材料，發現了 statin (lovastatin 、pravastatin、atorvastatin 、fluvastatin) 具有一些和降血脂無關的直接保護血管壁能力。包括會增加 interleukin-1β (IL-1β) 所誘導 iNOS 蛋白的表現及NO 的產生; statin 本身會增加 COX-2 和 HO-1 蛋白的表現及 PGE? 和PGI? 的產生，及抑制 MMP-2 和 MMP-9 蛋白活性的表現。此外分析調控 iNOS 基因轉錄最為關鍵的基因轉錄因子 NF-κB，發現適量的 statin 會增加 IL-1β 活化NF-κB 的作用。值得一提的是雖然適量 NO 有維持血管恆定的功能，過量時則會造成血壓過低休克的現象，這就是細菌感染後因內毒素 lipopolysaccharide (LPS) 作用引發敗血性休克的主要原因之一。為更進一步釐清 statin 是否會影響受細菌感染病人的生命危險，我們也探討 statin 對LPS 作用的影響。結果發現 statin 反而會抑制 LPS 誘導大量 iNOS 蛋白的表現，NO 的產生及 NF-κB 的活化。這些新的實驗結果提供更多證據支持 statin 可以藉由維持血管舒張，減緩血管壁的發炎反應，穩定動脈硬化斑的作用，以有效控制動脈硬化各個病程的進展。這發現能讓我們更透徹明白 statin 的作用，且對將來研發 statin 在心血管疾病方面新的臨床治療用途是有所助益的。 ;The 3-hydroxy-3-methylglutaryl (HMG)-CoA reductase inhibitors, statins, are potent inhibitors of cholesterol synthesis and have wide therapeutic use in cardiovascular diseases. Recent evidence, however, suggests that the beneficial effects of statins may extend beyond their action on serum cholesterol levels. In this study, we investigated the effects of lovastatin, pravastatin, atorvastatin, and fluvastatin on cultured rat vascular smooth muscle cells. We found statins can inhibit LPS-induced iNOS expression and NO production, while they can potentiate IL-1β-elicited responses. Moreover, statins themselves can stimulate COX-2 expression, PGE?, PGI? formation, and HO-1 induction. In contrast, statins can inhibit basal and IL-1β-induced enzyme activities of MMP-9 and MMP-2. In studying the activity of NF-κB, which plays an important role for iNOS gene induction, we found that statin can increase IL-1β-induced NF-κB activity, while inhibit that induced by LPS. All these results suggest that stimulation of iNOS expression in the presence of IL-1β, togeth1er with the increased COX-2 and HO-1 expression might contribute to the beneficial effects of statins in atherosclerotic process in terms of vasodilation and inhibition of smooth muscle cell proliferation. The inhibition of MMP activity might enhance plaque stability and reduce the development of atherosclerosis. All these results strengthen the pleiotropic actions of statins in anti-inflammation and anti-atherosclerosis.