上體育課的時候看到同學投空心球（籃球在沒有碰著籃框的情況下進入籃中），覺得好厲害。因此，我們利用相關的數學知識與運動原理來討論籃球投出後的運行軌跡，以及影響其命中率的相關因素。我們得知籃球的運行軌跡是一條拋物線，並求出其二次方程式；並利用標準籃球直徑與籃框直徑找出籃球進入籃框的最小入射角。若要提高命中率，必須考慮籃球投出時的投射角、初速度、籃球投出時的高度以及籃球與籃框水平距離之間的相關影響。此外，我們藉由電腦軟體列出相關數據提供作為實際投籃時的參考，並藉此進一步分析上述因素如何影響籃球運行軌跡以及如何提高投籃的命中率。Those who always shoot nothing but the net in basketball games were always heroes to me. I have being thinking for a long time how to become a person of that kind. For this, we investigated the trajectory of shooting a basketball and the factors to increasing the field goal percentages through our knowledge on mathematics and physics. We have obtained that the trajectory is in fact a parabola and, we further, found its quadratic equation. We also derived the minimal incident angle from the diameters of the standard basketball and hoop as well as the quadratic equation we have found. To raise the field goal percentages, some important factors must be taken into consideration, such as the vertical and horizontal distance between the basketball and the hoop, the incident angle and the initial velocity of shooting. Finally, we provide some concerning data for reference, and analyzed how the important factors we have mentioned above have affected our basketball trajectory and how, of the most importance, to increase the field goal percentages

在炎炎夏日總希望來點可以「降火氣」的食品，依據古籍記載某些中藥材具有降火氣的效應，而中醫所謂的降火氣與西醫的抗發炎反應密切相關。本實驗利用巨噬細胞株受到LPS (Lipopolysaccharide，革蘭氏陰性菌細胞壁表面所含有的脂多醣體)刺激後，會分泌發炎介質的現象，再分別加入各項傳統認為可降火氣(以菊花、薏仁、仙草作為樣品)或上火氣(選用龍眼作為樣品)的中藥食材，來評估中藥材對巨噬細胞分泌發炎介質能力的影響。經由實驗，我們發現市售的『降火氣』中藥食材，在適當的濃度下，確實具有降低IL-6、TNF-α 分泌量的能力，但濃度過高時卻會造成細胞凋亡。另外，傳統以水熬煮的方式比冷凍乾燥取得的樣品有更好的降低IL-6、TNF-α 分泌量的能力。 我們期望以此一系列的實驗，來建立篩選『降火氣』食材的抗發炎效用的研究模式，並在後續實驗中可用以篩選出更多具抗發炎效應的中藥材。In summer, people always consider eating some special things to refresh themselves. According to ancient books, there are some Chinese herbal medicines that were recorded to have the function of cooling us down, which is related to anti-inflammation in the Western. Macrophage cell lines can be stimulated by LPS (Lipopolysaccharide) and secrete proinflammatory mediators. Thus, it is often used to evaluate the anti-inflammatory effects of different herbs. In our experiment, we also use macrophage cell lines to test different anti-inflammatory effects between chrysanthemum, Job’s tears and grass jelly. In addition, some Chinese herbs such as longan that can parch us are also tested in our experiment. In our results, we found these herbs that are available indeed have ability to anti-inflame in appropriate consistency; however, high dose does harm to cells. In addition, the samples that are poached in ancient ways have better ability to show the low dose of IL-6 and TNF-α. Finally, we would set up a model to test the anti-inflammatory ability of different herbs that were said to be able to cool us down, and then we could test more herbs in the future.

吹長笛時，按同一按鍵，以大小不同的力量去吹，會引發不同頻率的泛音，而通常越用力吹，引發泛音的頻率越高，所以我們想了解為什麼越用力，泛音的頻率會高，其間的關係究竟是什麼？風經過管口會產生各種頻率的噪音，其中某些特定頻率的聲音會因為會在管內形成駐波而放大，所以我們只能聽到某些特定頻率的聲音。當風速增加時，會在管口形成渦漩逸放的紊流現象。其渦漩頻率與流速成正比（註一）。我們以塑膠管實驗。發現以特定的風速引發該基音後，繼續增加風速，當風速達某一定強度時，才會躍遷為下一個泛音的頻率。這個現象告訴我們：在一封閉管下，風速與泛音的關係並非「線性遞增」，而是越「躍遷遞增」的關係。另一個實驗測量不同管長、其諧音之頻率的關係，我們可以得知，越短的管子，因為相鄰兩泛音間頻率差較大，越不易激發更高階泛音。經由這些實驗結果，我們能夠推論：當管子越長、基音頻率越低時，諧音間頻率的差距相對越小，繪出的風速－頻率關係圖應更加顯示了風速與頻率呈正比關係。未來我們可以以閃頻器觀測紊流渦漩的產生，再變化至不同吹入角度，及各式管口造形，這些實驗能協助我們更進一步了解樂器的發聲原理，甚至開發一個以聲音頻率測量風速的儀器。註一：林婉如、張?文2006 國際科工程組佳作作品。When we press the same key and blow a flute using different strengths, we can get different overtones. Usually, the harder we blow the flute, the high the frequency we get. We want to understand why we get a higher frequency when we blow harder into the flute and to understand the relationship between them. When wind passes through the mouthpiece, many kinds of noises will be produced. Some of the frequencies will expand because they will form standing waves in the tube. Therefore, we can only hear certain frequencies. As wind speed increases, a turbulence of the vortex shedding will be formed. The frequency of the vortex shedding and wind speed will be in a direct ratio. We experiment with plastic tubes. When we increase the wind speed and get certain magnitudes, the frequency will jump to the next overtone. The phenomenon shows that the relation, in a closed tube, between wind speed and harmonics is not a linear increase but a transition increase. In another experiment, we measured the relationship between wind speed and different lengths of tubes. We can infer that the shorter the tube, the higher high-frequency harmonics can be produced. Through these experiments, we come to the conclusion that the longer the tube, the lower frequency of the fundamental tone we get and the discrepancy in frequency between harmonics is smaller. Then we make a diagram between wind speed and frequency that indicates that there is a direct ratio between wind speed and frequency. In the future, we can use “” to observe the production of turbulence. Then we can switch to different angles when we blow into flutes. Otherwise, we can experiment with different shapes of mouthpieces. These experiments can assist us to understand more how the instrument sounds. We can develop a device measuring wind speed with frequency.

This research tries to find out how changes of weight or proportion of a reactor would affect the type and structure of a crystal. In the experiment, the Hydrothermal reaction was adopted to conduct the syntheses of Vanadium-substituted Gallium Phosphates and try to pick up the single crystal to collect data with SXRD for further illustrating the crystal structure with diamond software to know well its nature. The research result finds out a new type of crystal unseen in the existing literature produced because of the weight changes of C3H10N2, therefore the weight change of a reactor may affect the structure of crystal significantly. In the future, it is expectation that comparison among structures of other Vanadium-Substituted Gallium Phosphates can be made, and the properties of this compound can be measured, and try to find out a brand new type of structure for new exploration by changing the initial reagent. 本研究係透過改變化合物所添加之反應物的比例，以了解反應物比例的改變對晶體的型態與結構的影響。實驗採用中溫水熱反應來從事金屬釩鎵磷酸鹽的合成。並挑取單晶，以X-ray 繞射儀進行數據收集，再以diamond 軟體繪出晶體的結構圖，且進一步得知其性質。研究結果發現，經改變丙二胺的量後，產生不同於文獻上的新化合物，可知改變所加反應物的比例，對於晶體結構有相當大的影響。未來可朝向與其他的釩鎵磷酸鹽做結構上的比較、對此化合物做更進一步的性質測量、改變起始試劑測試，進而得到更新穎的結構形式等部分進行探究。

本研究主要是以台北市中心的氣溫觀測站，以及市區外圍東邊的汐止，南邊的屈尺，以及西邊的山佳等三個氣溫觀測站，從1998 年至2004 年的七年期間的氣溫資料中，來探討台北地區的熱島效應現象。這個研究的結果發現，台北市區與周遭鄰近地區確實會因為熱島效應的影響而產生1~2℃的溫差。這個溫差在白天時不甚明顯，在中午過後，便由台北市中心逐漸向郊區遞減，形成類似同心圓狀的分布。溫差最大值發生在夜晚，使得台北地區晚間宛如一座夜晚增溫的城市，同時夏季的熱島效應又較冬季顯著，氣溫又逐年遞升，造成夏季台北市區的高溫屢創新高，將是未來都市發展的危機。This study is focused on the urban heat island effect of Taipei Basin, northern Taiwan. The hourly temperatures of Taipei meteorological station and three rural sites eastern Hsi-Chih, southern Cyu-Chih and western San-Chia, were compared from 1998 through 2004 to illustrate the temperature differences between city center and surrounding country areas. The results show that a difference of 1~2℃ exists between city center and surrounding country areas, indicating the extent of urban heat island effect in the Taipei Basin. The daily temperature contours show a clear high-temperature bull’s eye at the city center during the midnight, implying the high latent heat trapped by the dense and high rise buildings. This phenomenon is not sharp in the high noon due to the reduction of temperature difference between city center and surrounding country areas. The heat island effect is most prominent in the summer than that of the winter. Along with the increasing temperature-difference trend through years, the summer times often experience record-breaking heat waves and pose great risks for the city development in the future.

PURPOSE: The purpose of making an Inverter which gets charged with the help of sound energy, produced by speakers for instance, and regenerative shock absorbers which are used in cars so that we can easily charge the inverter with the help of sources which we use in daily life. PROCEDURE: The regenerative shock absorbers are capable of generating electricity when a car moves over bumps. It works by hydraulic fluid passing through a turbine. When the fluid passes through turbine, the turbine turns a small generator and more power is created. A piston is disposed for reciprocating motion within a cylinder as a vehicle’s suspension system deflects. Hydraulic fluid passes through a hydraulic motor to turn its shaft. The hydraulic motor shaft is connected to an electric generator to generate electricity. The second source of energy to charge the inverter is by the help of sound produced in day to day life. Some piezoelectric sensors attached to the board as soon there is a tap or any kind of vibration on the board these and convert them to electrical signals. This means that parasitic energy of busy roads, railroads, footpaths and runways near population centers can be converted into electrical energy that can run public lighting, or fed back into the grid. DATA: The data which have been collected with some experiments is that on an average piezoelectric can produce 330W of power. • When sound pressure is around 62 dB, the frequency is of 102 Hz. • Sound pressure is of 65 dB the frequency is of 500 Hz. Another case when the regenerative shock absorbers come in contact with the piston it produces an average power of 340W-350W. CONCLUSION: With the use age of piezoelectric sensors and regenerative shock absorbers we can produce electricity at a very low cost for inverters; these inverters can provide electrical supplies to the house. The most important reason to make such kind of innovation is one because it is money efficient, second this can come in handy for those who can’t afford to buy inverters at a very high cost and then when charging these inverter these people have to use their electrical supply!

本研究的目的在觀察液滴的蒸發過程，探討影響一滴蒸發方式改變的變因。我們利用數位攝影機外加近攝鏡頭，由側面逆光拍攝液滴蒸發過程，並轉錄成電子檔利用電腦協助分析。液滴影像分隔放大投影在方格紙上，以便測量接觸角及高度的變化。結果發現蒸發情形可分為三種：Ⅰ.當接觸角大於九十度時，液滴和界面的接觸線迅速外擴，直到接觸角遞減至90度後定住不動，蒸發終了時，接觸線迅速內縮，留下縮小的實心殘跡。Ⅱ. 當接觸角小於九十度時，接觸線先些微外擴迅速外擴，之後定住不動，直到蒸發終點，液體內縮，留下環狀殘跡。Ⅲ.當接觸角小等於九十度時，接觸線始終定住不變，液滴蒸發後留下原大小的實心班跡。液滴蒸發時接觸角和高度並不是連續變化，而是交互階梯式遞減。本研究的結果可應用在探討噴漆及噴墨印表機的噴墨印刷上。The objective of this investigation is to observe the evaporation of liquid drop and find out the factors that could affect it. A digital camera with micro lens is used to film the process of the evaporation. And a close-up of the sample drop is taken with backlight. The results are analyzed with a personal computer. The magnified images of the drops are projected on grid papers for measuring the changes on contact angles, and heights of drops. We classify the evaporation of a drop into three types: Ⅰ. The contact angle is greater than 90 degrees. At first, the contact line will spread outwardly till the contact angle decrease to the 90 degrees and then be pinned until the evaporation reach its terminal. At last the contact line quickly contract inwardly, and a solid stain remain. Ⅱ. The contact angle is less than 90 degrees. The contact line will spread slightly and then be pinned. At the terminal the liquid contract inward, and a ring-like stain is formed. Ⅲ. The contact angle is equal to 90 degrees. The contact line will always be pinned, and no ring, but spot stain is left. During the evaporation, we discover that the contact angle and the height of the drop do not change continuously but alternatively decrease by steps. The results of our investigation can be applied to the aspects of paint-spraying and jet printers.

含羞草會因為受到各種不同外界刺激(光照、外力等等)，而造成膨壓改變。外 觀上表現出葉片閉合或有葉柄下垂的現象。其中含羞草處在黑暗的環境下一段時 間後，會做出睡眠運動。當它重新暴露於光照之中，將會需要一段時間以恢復原 先葉片張開的樣子。這個實驗是研究不同類型的環境因子(主要是光照和溼度)在打 破睡眠運動之後，對其葉片復原時間所造成的影響。我們針對上述環境因子在不 同狀況時，進行我們的實驗上百次，進一步得到了多項的數據。也在實驗中，為 了精確了解整個恢復的程序，而將恢復程序程序做成書面說明。以下是我們所紀 錄與分析完數據後的結果，以及我們在實驗期間，進行一些不同的實驗嘗試，所 發現不同於表面所見的驚人事實。 The mimosa can accept plenty of stimulation (light, force, etc), which results in the change of turgor pressure, and on outward appearance, it shows the phenomenon that the leaves become closed or that the stalks get pendent. Among the stimulation, the mimosa will undergo nyctinasty when it is left in the dark for a period of time, in order to enable it to be exposed to the light once more, which requires certain time. This experiment is based on how different kinds of elements of the environment (primarily light and hydro level) effects the rehabilitation time after the nyctinasty is broken. A large number of data are gained after experimenting on it for hundreds of times. Steps of habilitation are also made into illustration in writing, so as to understand the whole steps accurately in the experiment. Below are our records and analysis based on the data, including a few special experimental tries during our working time, in which some surprising facts that were discovered are different from what are seen on the surface.

關於平面上若干點的集中度之定義，一直很少有人予以仔細的探討，因為判別的方法有很多種。本研究是以平面上三點所構成的三角形之三頂點作討論，分別以三角形的面積、周長，內心、外心和重心至三頂點距離，三點的標準差及平均差的概念，作為不同的判別方式，並以動態幾何化版ＧＳＰ模擬不同的判斷方法做為研究，在利用統計學上的方法，找出哪一種定義方式最為適合、誤差最少的判斷方法。There are many ways to determine the centralness of three dots on a plane; however, no definition study has been applied. In this study, we focus our interests on the entralness of three vertices of a triangle formed from three dots on a plane. Various methods such as the relationship of area, and the distance of the triangle to the centralness of three dots, the distance from the interior point, exterior point, the barycenter to the vertices of triangle, and the standard error and differences average obtained from three dots were determined with a dynamic geometry software GSP, and a statistic method was used to find a least error way to determine the centralness of three dots on a plane.

細胞脂肪分化是造成肥胖、骨質疏鬆、和糖尿病的重要前置因素。我們若要維持良好身材又想省去減肥藥的問題，那麼我們必須了解造成脂肪化的原因，才可能擁有好的預防之道。利用人類骨髓間質細胞可以分化成骨質與脂肪等細胞的特性，我們研究氧化壓力對間質細胞\r Ras基因轉換表現後骨質與脂肪分化的影響。結果發現以添加超氧根 (O2-，l5nM)形成氧化壓力，可促進正常Ras基因表現的間質細胞朝骨質分化;相反地，超氧根會促進\r Ras基因突變而不表現的細胞，朝向脂肪分化的現象。進一步研究其作可原理，發現氧化壓力可促進 RaS蛋白質啟動細胞外訊息活化酵素(ERK)，接著驅動骨質轉錄因子(CBFA1)表現，再到骨鈣蛋白質與骨結節形成。而抗氧化酵素(超氧根轉化酵素;SOD,5OOU/ml)的作用，可以抑制正常Ras基因細胞氧化壓力下骨質分化的進行;但不能防止氧化壓力促進Ras基因突變細胞，朝向脂肪分化的作用。總結而言:Ras基因的表現與否，是決定脂肪分化的關鍵切換點;也是影響氧化壓力對間質細胞朝骨質分化的樞紐。這種基因與氧化壓力互動影響骨質與脂肪分化的剖析，將有助於提醒人們:使用抗氧化劑來調節抗衰老、肥胖、和美容時，必須是在不同情況和不同基因體質的人，有所不同。 \r Human\r mesenchymal stem cells are able to differentiate into bone, muscle, cartilage or\r fat tissues. Our preliminary study with human mesenchymal cell line (HS-5) showed\r that HS-5 cells could differentiate to bone, cartilage and muscle but not fat cells\r as determined by histochemical staining of phenotypes. We have further studied the\r influence of oxidative stress on the switch between bone and fat cell differentiation.\r Results showed that oxidative stress started with exogenous superoxide, produced\r by the interaction of xanthine oxidase and hypoxanthine, promoted the differentiation\r of osteogenic lineage showing expression of osteocalcin and bone nodule formations.\r The mechanism was investigated and superoxide was found to induce ERK (extracellular\r regulated signal kinase) activation; and then the expression of osteogenic specific\r transcriptional factor (CBFA1). A plasmid containing ras-mutant (Ser 17 Asn) which\r can inactivate the expression of ERK was transfected into the HS-5 cells for studying\r the influence of oxidative stress on ras-mutated mesenchymal cells. Surprisingly,\r it was found that oxidative stress did not promote osteogenesis but it enhanced\r adipogenesis from the ras-mutated HS-5 cells. Further studies indicated that superoxide\r neither induced ERK activation nor CBFA1 expression, but it did enhance expression\r of adipogenic specific transcriptional factor (C/EBPα) and lipoprotein lipase in\r the ras-mutated mesenchvmal cells. Taken together, the study model to induce the\r bone cell differentiation from human mesenchymal stem cells may be employed to make\r bone cells for tissue engineering.

「翻車」事件令人怵目驚心，輕則車毀，重則人亡。減少翻車事件，可減少悲劇的發生。而翻車絕大多數均發生在轉彎的路段，且伴隨著超速發生。因此，本研究乃針對汽車過彎行駛，探討其翻覆的原因以及改進之道 · 本研究乃利用實驗分析法以及理論驗證法進行研究，實驗中變化不同的汽車質量，車軸寬、車身高以及車軸寬/車身高，質量重心寬、高以及寬/高、傾斜度以及迴轉半徑等九種參數 · 於自製的紅外線偵測變頻式可調迴轉模擬機上以八部模型試驗車測試其翻覆轉速，並換算為翻覆速度後逐一分析討論之。經由實驗結果，本研究得到以下結論：一、汽車轉彎翻覆與離心力有關，當離心力大於臨界側向推力時，汽車即翻覆。臨界側向推力公式為 F = mg ( tanθ + K?) / ( l -K? tanθ ) 二、最大容許車速平方與轉彎半徑及質量中心寬高比相乘積成正比；而在定車速下，飲小客許轉彎半徑與質量中心寬高比成反比．前述各項皆與質量大小無關．三、提高轉彎路面傾斜度對防止汽車翻覆有確實的效果。而最佳的過彎防止翻覆方法是降低車行速度，提高轉彎半徑，增加路面外側傾斜度，以及提高汽車質量中心寬高比”四、汽車過彎不致翻覆的最大極限速度 Vc 以及最小轉彎半徑rc分別為 vc=〔 rg ( tan θ + K ?）/ ( l 一 K ? tanθ ) ]; rc =（ V2 / g ) ( l 一 K?tanθ ) / ( tanθ + K? ) 五、本實驗所設計紅外線偵測變頻式可調迴轉模擬機，可有效的模擬汽車過彎翻覆，適用於中等學校物理、力學等學科的實驗課程。The accident of overturning a car always results in both destroying the car body and the death of the people. This project is to investigate what factors would have an effect on overturning a car and how to prevent a car from overturning.This project explores the factors by varying the mass of the cars, the distance between axes, the height of the car body, the ratio between the axis distance and the car height, the central gravity, and the declination. We test and record different overturning rotating speeds of eight model cars by a self-made adjustable simulator with a varying frequency infra-red detector. According to the experiment, the following results are obtained. I. The overturning occurrence is as a result of the eccentric force over the critical lateral force. The critical lateral force is F=mg(tanθ +K?)/(l—K?tan θ) 2. The square of allowable maximum speed is in proportion to the product of turning radius and ration of width to height for the center of mass; however, the allowable minimum turning radius is inversely proportional to the ration of width to height for the center of mass under constant vehicle speed. The above inference is independent of the mass of vehicle. 3. Increasing the declination can prevent a car from overturning. 4. The maximum speed for a car turning without overturning is Vc. The minimum turning radius is r. Both are expressed as follows:Vc=[rg(tanθ +K2)/(1—K?tanθ );rc=(’V2/g)( I —K?tanθ )/(tanθ +K?)5. The self-made adjustable simulator with a varying frequency infra-red detector can be used in the experiments of the middle school science curriculum.

在夏日的午後，在炎熱的柏油路面上很容易可觀察到遠方的 路面上，出現如鏡子般的倒影，看起來彷彿前方有一灘水，但當 我們向前進一些時，倒影卻突然消失了，這個現象，一般稱為海 市蜃樓。 一般解釋海市蜃樓的成因，都是由於在上層的低溫空氣，和 在下層靠近路面的高溫空氣，因密度的不同，以致於折射率的漸 層差異，繼而產生全反射。 但我們觀察發現，地面與上層空氣的溫差，並非柏油路面上 假積水現象及倒影出現的必要條件；反而和入射光的角度、路面 的平坦程度及路面的性質有關。我們提出了粗糙面在入射光的入 射角接近90度時，可發生單向反射的模型。並由實驗來驗證假積 水現象及倒影主要的成因是「柏油路面的單向反射」而非「空氣 的折射與全反射」。 Under the scorching sunshine, we can see the reflection on the tarmac in the distance just like a water puddle on the road. And the water also reflects the people and object nearby. But, in fact, the tarmac road over there is very hot and dry. Therefore we call the phenomenon as the “false water puddle on the tarmac.” According to the textbook , the main reason for “false water puddle on the tarmac” is that the temperature difference leads to the refraction of the light and causes the phenomenon. However, from our observation, the theory still can’t explain some phenomenon, For example, the “false water puddle on the tarmac” remains to appear when the wind blows fiercely. Even with little temperature different at night the phenomenon is still obvious. Therefore, in our opinion, the temperature different of the air is not a necessary condition of “ the false water puddle on the tarmac.” We bring up the model to explain the phenomenon that when the incident angle of the light approach 90 degrees, the light will result in one-way reflection. According to the model, furthermore, we make experiments at midnight and at dawn. The result of the experiment assures us the hypothesis of the model, Consequently, we hold the ideal that the main condition of the “false water puddle on the tarmac.” Is not because of the refraction and the total reflection but because the light reflects off the road and result in the one-way reflection on the tarmac road.