本文我們研究下列問題： 1. 何時心律會成穩定的狀態呢？ 2. 是否能建立出心律穩定的數學模型？ 3. 什麼樣的函數會使得心律趨於穩定？我們以xmp+i 表示第p+1 個訊息傳到第i 個細胞之前，第i 個細胞的舒張時間，而且xk 和 xk−m, xk−m+1,..., xk−1的關係為 In this paper we study the problems as follows: When will the rhythm of heart beats approach to a steady state? Can we set up the mathematics model with steady rhythm of heart beats? What kind of function will make the rhythm of the heart beating tend to be stable? The result of our study is as follows:

本實驗是以實際探勘的地質及泉水資料和文獻為基礎，對於幾個可能造成冷泉降溫的原因(岩石種類、泉水pH值、流通氣體之壓力、流速)進行實驗。我們製作了一個模擬地下泉水流動的實驗管路，此管路並可同時觀察紀錄氣壓、氣體流速，以及實驗前後模擬管路的溫度變化。透過對實驗管路的熱容量校正，我們可以找出各變因對泉水降溫的關係，以建立出一個模型，期望可套用於實際冷泉的狀況，進而推論出更多冷泉的性質。This experiment uses data and bibliography from real exploration as bases to find the possibilities of why the cool spring drops in temperature. (Mineral types, spring water's pH value, air flow pressure, and movement flow.) We created a model of underground spring water for the simulation. From this model, we could observe the air pressure, movement, and the spring's change of temperature before and after the tests. By adjusting the thermal capacity in the model, we could find the direct cause of the spring's temperature drop. And hopefully be able to adopt this model to the realistic problem, increase the effort of analyzing the natural cool spring's properties.

這份報告的主題是藉由實驗，來探討雷射光的性質及它的應用，並實際製作利用雷射光原理的小器具。1.證明雷射光是否為單色光：先將雷射光射入不同顏色的玻璃紙，利用光無法穿透不同顏色玻璃紙的性質，以及將雷射光照射三稜鏡，觀察其反射的光線，藉此來證明雷射光是否為單色光。2.雷射光的直進性質：利用彎管或其他不透光物品將光線阻擋，觀察其是否能穿透物品，並且用不透光物質，使我們能夠看出雷射光的軌跡，來證明雷射光的直進性質。3.雷射光的折射與反射：將雷射光射入不同的物質中，觀察其折射角度，來得知雷射光在不同介質中的傳播速率不同，也觀察其是否有反射的現象。4.雷射光的應用：研究運用雷射光製成的物品，如雷射印表機、光碟機等等，並了解其製作原理。5.自行研製雷射小器具：利用雷射光的原理，來製作簡單而獨特、有效率的小器具。The topic of this report is to study the quality and applications of laser by experiments, and actually make a tool by using the principles of laser.1.Prove if laser is a one-color light: By lasing laser through a triangular prism, observe the light it reflected to prove that laser is a one-color light.2.The quality of in-line approach: By using tubes or other lightproof items to block out the light to observe if it can penetrate things, and also let us see the trace of laser to proof the quality of in-line approach.3.The refraction and reflection of laser: Study the differences of refracting angles by lasing laser into different items, to know the speed of laser in different mediums, and also observe if it will have any reflections.4.The applications of laser: Understand how laser products are made by studying them, like laser printers and CD players. 5.DIY laser tools: Make simple but unique and efficient tools by using the principles of laser.

溶液和溶劑置於同一容器中，當溶質向上擴散時，會形成濃度梯度及\r 折射率梯度dn/dy，且dn/dy 對高度y 的關係圖會呈現隨著高度改變的現\r 象。\r 半徑r 的Ｄ形容器，下方置溶液，上方置溶劑，以雷射光照射容器的\r 平面部份時，雷射光沿著法線出射，受折射率梯度的作用而向下偏Ζ距\r 離，a 為容器至屏的距離，得到dn/dy=Z/ar 的關係式；改變雷射光的高\r 度y 可得dn/dy 圖。\r 以硫代硫酸那作實驗，其dn/dy-y 圖為以原始界面為對稱軸，因其擴\r 散係數不隨濃度改變；甘游水溶液的dn/dy-y 圖呈現不對稱，圖形的極\r 大值往甘油方偏，主要係因為甘油的擴散係數隨濃度的增大而減少。\r 我們成功第把不同時間對同一溶液的實驗結果予以模型化，得到的\r dn/dy-y 曲線隨時間改變，並發現該曲線所涵蓋的面積為定值。\r \r The mixing in a vertical column between a pure liquid and a solution produced a concentration gradient, which in turn produced the refractive index gradient. As the solute particles diffused upward into the pure liquid, the gradient was generated by the varying solute concentration. The plot of the refractive index gradient versus vertical position y (dn/dy vs y) is found to be varied with time. A D-shape container of radius r is partly filled with denser solution, and partly filled with solvent which is on the top of solution. When laser beam enters perpendicularly to the flat surface of the container, the outgoing beam strikes the container at normal incidence, and deflected down a vertical distance Z by the refractive index gradient. We can get dn/dy=Z/ar, where a is the distance between the container and the screen,. By changing the vertical position (y) of laser beam, we can get the plot of dn/dy vs y. For a sodium thiosulfate-water solution, the trace of dn/dy vs y is symmetric with respect to the position of original boundary. Since the diffusion coefficient of sodium thiosulfate is independent of concentration. For the trace of dn/dy vs y of a glycerol-water solution, it will no longer be symmetric. A skewed curve which reaches its maximum position is displaced to the glycerol side, because the diffusion coefficient of glycerol is decreased with concentration. We have successfully modeled the time-dependent experimental gradient curves on the same solution. The trace of dn/dy vs. y at different time is found to keep the area constant.

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：

本研究目的主要在瞭解昆蟲的複眼(compound eyes)結構，比較晝行性與夜行性昆蟲複眼之差異，探討其視覺遠近和複眼結構的關連，及進一步觀察其對不同波長光源反應的差異。本實驗使用反射式及倒立式顯微鏡來觀察複眼及其小眼的結構，及觀察其成像情形，並使用攝影式接觸分析儀與放大管來探討視覺遠近和小眼表面曲率之關連，另外在暗室利用不同波長的光源照射蝴蝶以觀察其反應。實驗結果顯示複眼是由數千至數萬個小眼組成，小眼表面曲率半徑隨選用物種在25.3μm 至117.6μm 之間，蜻蜓複眼上半部和下半部小眼曲率半徑分別為30.6μm、117.6μm，印證了蜻蜓複眼上看遠下看近的說法，也發現蝦子小眼是正方形，其他實驗物種則皆為六邊形，而蝴蝶對光的反應程度則是隨波長漸增而遞減。The main purpose of this study is to understand the structure of the compound eye of insects, to compare the difference between the diurnal insect’s compound eye (apposition eye) and that of the nocturnal insect (superposition eye), to explore the relationship between the vision and the structure of the compound eye, and to observe the eye’s reaction to the different light wave length. In this study, a microscope (OLYMPUS BX51M) and an inverted microscope (OLYMPUS 1X71) were used to observe the structure of the compound eye and its ommatidia, as well as the resulting image. A contact angle measuring instrument (Dataphyscis OCA 20) and a microscope (Mitutoyo NAVITAR) were used to determine the connection between the vision distance and the facet curvature of ommatidia. The butterfly’s reaction to the light source with different wave length was also observed in a darkroom. It was observed that the compound eye of insects is composed of more than a thousand ommatidia. Among the subject insects, the facet curvature radius of their ommatidia ranged from 25.3μm to 117.6μm. The radius of the top and bottom half of a dragonfly is 30.6μm and 117.6μm. It confirms a scientific finding that dragonfly’s top compound eye focuses farther than the bottom half. The facet of each ommatidium observed is hexagonal in insects compared with the square shape found in the eye structure of shrimp. Regarding the reaction to light of the butterfly eye; the reaction decreased when the light wave length increased.

利用范式起電器將靜電導入蒸餾水、甘油、苯、環己烷、乙醇、正丙醇、正戊醇，以及HCl(aq)、NaCl(aq)、CuSO4(aq)……等不同溶液中，我們發現：非電解質溶液可以藉由極性分子的媒合作用"貯存”電子，而其中H2O效果最好，即水合電子是可以穩定存在的！但在水中若添加HCl、NaCl等電解質會提高容易導電性，以致於無貯存電子的效果。我們也發現苯雖不是極性分子，但因具有π共振系統，也能有效貯存電子。另外，從引入密度泛函數理論結合類導體可極化連續模型加以計算的結果，也能發現極性分子容易的溶劑電子親核能比非極性分子容易來的大，與實驗結果吻合。By using a Van de Graff Generator to put electrons into various solutions or solvents (such as water, alcohol, benzene, propyl alcohol, solutions of sodium chloride, etc.), we find out that nonelectrolytes can "store" electrons through hydration of polar molecules. And water has the best ability of keeping electrons among others. In other words, hydrated electrons can exist stably. However, if we add electrolyte into solvent, the solution won't store electrons because of its increasing electric conductivity. The experiment also shows that benzene can keep electrons though it is a nonpolar molecules. We infer that it is the " π resonance system " which contributes to its high ability of electron storage. In addition, by introducing the calculations of CPCM (Conductor-Like Polarizable Continuum Model), we find out that the electron affinity of polar solutions are stronger than those of nonpolar solutions. The computed results are in agreement with our experiment.

重金屬對人體傷害的無遠弗屆-人人皆知，根據流行病學的研究指出，長期處\r 在重金屬含量過高之地區，易造成生理病變。比方說，長期生活在砷含量高的環境\r 中，易導致肝臟、周邊血管及神經系的損害，各種癌症的發生機率也大為提高；長\r 期處在含量過高的鎘環境中，易引起不正常的鈣代謝﹐產生骨質疏鬆症、軟骨症、\r 糖尿、胺基尿酸、尿蛋白、貧血、和肝功能異常的症狀；而目前坊間所看到各類茶\r 品中含有的兒茶素則被發現具有抗氧化、抗突變及清除自由基等功能。故本實驗以\r 人類胃癌細胞(SC-M1)為材料，以微核(micronuclei)偵測技術觀察細胞長期處理兒茶\r 素((-)-epigallocatechin-3-gallate, EGCG)後，對於亞砷酸鈉(sodium arsenite, NaAsO?)\r 及氯化鎘(cadmium chloride, CdCl?)所造成的細胞遺傳毒性有何影響。另一方面則利\r 用SRB 分析法測量細胞存活率，探討長期處理兒茶素後，亞砷酸鈉及氯化鎘對於細\r 胞的毒殺情況是否改變。實驗結果顯示細胞長期處理兒茶素不會造成微核的增加，\r 但是卻會增加細胞的存活率；單獨處理亞砷酸鈉和氯化鎘則都會使細胞中微核明顯\r 的增加，且會降低細胞的存活率；而長期處理兒茶素的細胞對亞砷酸鈉所誘發的微\r 核有抑制作用且會增加細胞對於亞砷酸鈉的耐受度，長期處理兒茶素無法抑制氯化\r 鎘所誘發的微核與細胞毒性。\r \r \r It is well documented that exposure to heavy metals could cause seriously adverse\r effects to humans. Epidemiological evidence has shown that illness is frequently\r observed in residents living long-term in heavy metal contaminated area. For example,\r long-term exposure of arsenic was associated with increased incidences of liver diseases,\r peripheral vascular and neurological diseases, as well as cancers. And long-term exposed\r to cadmium may lead to abnormal metabolism of calcium, osteoporosis, osteomalacia,\r glucouria, aminoaciduria, proteinuria, anemia and abnormal liver function. Recently,\r numerous reports have shown that (-)-epigallocatechin-3-gallate (EGCG), the major\r polyphenol from green tea, have ability to anti-oxidative stress and anti-mutagenesis. In\r this report, we investigated the effects of EGCG long-term exposure in sodium arsenite\r and cadmium chloride induces chromosomal damages and cytotoxicity in a gastric cancer\r cell line, SC-M1. Our present results demonstrated cells long-term exposure to EGCG did\r not induce micronuclei (MN) formation but induce the growth rate. Sodium arsenite or\r cadmium chloride alone significantly induced MN formation and cytotoxicity in cells\r without long-term EGCG exposure. However, long-term treatment of SC-M1 cells with\r EGCG significantly reduced MN formation and protects the cells from cytotoxicity\r induced by arsenite. Long-term exposure of EGCG had no effect on MN induction and\r cell survival in cadmium-treated SC-M1 cells.

本實驗一開始主要探討超聲波在水中的基本性質，如：指向性、衰減性…等。實驗發現，超聲波的衰減會同時與其指向性以及衰減性有關。 接著希望利用超聲波在水中的物理性質，近一步測量超聲波在水中的聲速，實驗中則利用駐波以及聲光效應測量。在駐波法測量聲速的實驗中，用洗淨機當作聲源，內部放置量筒，量筒內盛水後放入木屑，並使聲波在其中產生駐波即聲浮現象，求出波長後反推聲速，測量出的聲速誤差值僅有1.13%，而在使用聲光效應測量聲速的實驗中，使1.65 MHz 的超聲波在自製的壓克力容器內部所裝的水中產生駐波後，以波長650 nm 的紅光雷射通過，在遠處屏幕即產生似於光柵繞射現象，藉著屏幕上的繞射條紋反推該液體聲速，測量出聲速誤差均在5%以下。 在觀察聲光效應實驗中，發現過段時間後有氣泡產生，由文獻上，得知此現象為超聲空蝕現象(Acoustic cavitation)，就設計實驗測量聲場中聲壓分部，並利用蠟紙觀察氣泡的成長。實驗發現聲場中的聲壓強度以及液體的表面張力和蒸汽壓會影響到產生空蝕的臨界值及產生氣泡的數量。 ;At the beginning this experiment explores the ultrasonic base in the water, including its velocity, the physics property of liquid, direction, and attenuation etc. . . At first, we use methods of standing wave to measure the velocity of sound under the water, using an ultrasonic cleaner as the sound source and putting some wooden powder in the water. As the standing wave accrues/produces, the powder will “stand still.” To measure the length between two grains of powder, in this way we can calculate sound velocity. Another method we use is diffraction of optics. Put 1.65 MHz source and water in a transparent container; then using laser through it. At the board much diffraction light stripes are created. By this way, we can estimate the velocity. Following these ways can calculate velocity precisely. In these experiments, some bubbles create in the container are discovered. We learn it is so-called “Acoustic Cavitation” based on the reference paper. Besides, we design experiment to know the bubbles’ growth and the number of the bubbles is connected to the physics property of liquid. We use different kinds of liquid with different vapor pressure and surface tension. Finally, we know when it has the smaller surface tension and bigger vapor pressure, the liquid makes bubble velocity grow faster and larger amount of bubbles are produced.

當世界各國正全力朝奈米科技發展，而奈米微粒對環境及人類健康影響與否未明朗之際，有關奈米微粒對人類健康影響之探討是刻不容緩之事。本研究的近程目標是合成金奈米粒子，遠程目標是擬探討金奈米粒子的生物毒性。此份研究主要是描述金奈米粒子的最大表面電漿吸收光譜特性及其最大吸收波長，而金奈米粒子的合成是利用四氯金酸( HAuCl4 )與還原劑—硼氫化鈉( NaBH4 )、聯胺水合物( N2H5OH )或檸檬酸鈉在陽離子界面活性劑的溶液( CH 3(CH2)15N+(CH3)3Br– ，溴化十六烷基三甲基銨，CTAB ) 當保護劑中，利用氧化還原方法直接生成金奈米粒子，並探討四氯金酸的濃度、還原劑的濃度、界面活性劑的濃度及反應溫度，對金奈米粒子生成之影響，另外也探討金奈米粒子的穩定性。有關金奈米粒子的光譜特性則利用UV/Vis 光譜儀測試。研究結果發現在相同的條件下，利用冰浴，以NaBH4 當還原劑所合成出的金奈米粒子之平均粒徑為11.70 nm ，而以N2H5OH 當還原劑所合成出的金奈米粒子之平均粒徑為20.25 nm， 有關金奈米粒子之結構及大小藉由穿透式電子顯微鏡( TEM ) 拍攝出的影像得以驗證。;This study mainly focused on the properties of the maximum surface plasmon absorption of gold nanoparticles and their wavelengths. The synthesis of gold nanoparticles made use of HAuCl4 aqueous solution and reducing agent, through the oxidation reduction method, with reductant, sodium borohydride ( NaBH4 ), hydrazine ( N2H5OH ) or sodium citrate solution in the presence of the cetytrimethylammonium bomide ( C19H42BrN,CTAB ) aqueous solution as protecting agent. The influence of concentration of HAuCl4, reductant, surfactant, and temperature on the synthesis of gold nanoparticles were explored. In addition, the stability of the gold nanoparticles was also explored. Measurements of spectral properties of gold nanoparticles were done by UV/Vis spectrometer.When NaBH4 was used as a reductant, the average diameter of gold nanoparticles was 11.70 nm. When N2H5OH was used as a reductant, the average diameter of the synthesized gold nanoparticles was 20.25 nm. The structures and sizes could be identified by the transmission of electron micrograph (TEM) images.