一些Moire patterns 的數學性質研究
Moire 為法文，其英譯為watered， 是古代織布技術的一種應用；將印有規律條?的透明薄片重疊時，稍微移動或轉動其中的一片，會形成極大的圖形變化，稱為moire pattern本作品針對三個moire pattern 的數學式加以推導：(一)、兩張透明片各印有等間隔平行線，轉動其中一片使兩線的夾角θ，亮紋垂直距離和暗?垂直距離的比值為tanθ/2tanθ 。(二)、兩張透明片各印有輻射線，重疊後行成圓系，可由代數或幾何加以證明，利用三角函數可推導出此圓系方程式為：x2+{y-rtan[π/2-(θ-?)]}2)]}={rsec[π/2-(θ-?)]}2)]}\r \r (三)、透明片A 印有等間隔平行線，B 印有符合高斯曲線的平行線，AB 重疊時，形成一系列的高斯曲線，AB 的夾角減少時，會增大曲線的曲率，我們進一步討論曲線的曲率和平行線斜率的關係。Moire is the French word “watered” and refers to an ancient technique employed in cloth making. The moire occurs whenever two or more transparent sheets with periodic strips on them are superposed. The characteristic of moire patterns is the fact that a slight shift of sheets will create dramatic alternations in the observed patterns. In the present report, We derive the equations of three different moire patterns. First of all, take a sheet with equal spaced straight lines and placed it on top of another identical sheet. They are made to intersect and form an angle of θ. As the angle changes slightly, it produces huge changes in the spacing of moire fringes. We can derive a formula related to the interfringe distance. The ratio of bright fringes and dark fringes is tanθ/2tanθ.Secondly, two transparent sheets with radial lines on them are overlapped, forming a pattern similar to the lines of force between point charges. We can find that the pattern is a series of circle by means of algebraic and geometric proofs. And proven by trigonometric functions, we canconclude that they satisfy the equation :x2+{y-rtan[π/2-(θ-?)]}2)]}={rsec[π/2-(θ-?)]}2)]}\r Thirdly, a set of lines of equal spacing is overlapped with a second set of lines whose spacing are derived from a Gaussian curve. A series of Gaussian curves is reproduced in a moire pattern. Reducing the angle of intersection between the two figures steepen the curvature. We discussed the relation between the curvature and the slope of inclined lines.
氣候變遷對台灣地區異常降水的影響
Drought and inundation are two unusual natural disasters in Taiwan. The two natural disasters\r have some relation of abnormal rainfall become more and more in Taiwan. So it let me think about\r can climate vicissitudes make the chance of abnormal rainfall become more?\r The study have researched the chance of abnormal rainfall by "rainfall duration" and "total\r rainfall". It collect the day by day total rainfall from 1960 to July 2002, collect locals are Taipei,\r Taichung, Kaohsiung and Hualien. Than enter the data into the computer, let computer calculation\r total rainfall, rainfall days, heavy rain days, pouring rain days and torrential rain days. Then\r analysis the tendency of long-term change.\r According to the analysis, the chance of abnormal rainfall happened become more in Taipei,\r Taichung, Kaohsiung and Hualien. The ratio of Hualien and Kaohsiung is the most obviously. It's\r also find that there temperature and total evaporate became higher, the total sunshine duration\r became lower. Then El Nino have some influence in abnormal rainfal. In El Nino year, total rainfall\r will become lower. When La Nina year, the total rainfall will become more in Taipei and Hualien.\r Then the long influence is clearly in Taipei.\r 乾旱與水災是台灣地區相當常見的二項天災，這二項災害的發生都與異常降水有直接的\r 關係。近年來台灣地區因異常降水造成的天然災害，似乎有逐年增加的趨勢。因此讓人聯想\r 到氣候變遷是否會導致異常降水頻率增加。\r 本研究主要由「降雨時數」與「降雨量」二方面探討異常降水發生頻率。先收集台北、\r 台中、高雄、花蓮四地自1960 年至2002 年七月三十一日之逐日雨量資料，將資料輸入電腦\r 後，統計各站歷年降雨量、降雨日數、大雨、豪雨、暴雨日數，並分析長期變化趨勢。\r 分析結果，台北、台中、高雄、花蓮四地異常降水發生機率，有增加的情形；其中以花\r 蓮及高雄變化的比例最高。再與其他各地氣象要素比較可發現，可能與氣溫及蒸發量數上升，\r 以及日照時數縮短有關。另外聖嬰現象也可能對異常降水有長期性的影響。一般而言聖嬰年\r 雨量減少，反聖嬰年台北、花蓮地區雨量反而會增加。而長期性的影響，以台北地區最顯著。
安非他命對小鼠中腦紋狀體之細胞凋亡相關蛋白質表現的影響
安非他命的濫用在台灣是非常嚴重的公眾健康及社會問題。安非他命會導致一連串的行\r 為異常，包括在中腦紋狀體內釋放多巴胺及阻止多巴胺回收來增加使用者的活動力。由於安\r 非他命會對腦細胞造成傷害，本研究的目的為探討低劑量、無立即毒性之安非他命(類似於人\r 類使用習慣)於短期內是否會對老鼠大腦紋狀體內的蛋白質表現有影響。因此利用西方點墨法\r 分析施打低劑量安非他命(2 到6 mg/kg)約一星期之後，C57BL6 小鼠的大腦紋狀體中一些重\r 要蛋白質[包括腺?酸受體A2A-R、第五亞型腺?酸環化?AC5、caspase-8、PARP、NF-κB\r 及血紅素加氧?-1(HO-1)]的表現是否有改變。實驗結果顯示，低劑量安非他命處理對大部分\r 蛋白質的表現並沒有明顯的差異，但在施打安非他命老鼠之大腦紋狀體中，HO-1 有些微但明\r 顯的增加，顯示安非他命可能對腦組織產生氧化性傷害。因此長期使用安非他命對中腦紋狀\r 體是否造成傷害是值得關心及繼續探討的課題。The wide spreading use of amphetamine (AMPH) in Taiwan has become a serious\r public health and social problem. AMPH evokes a series of behavior abnormality including\r enhanced locomotor behavior by releasing dopamine and inhibiting dopamine-uptake in the\r striatum. Since AMPH is known to cause brain damage, the purpose of this study is to\r investigate the expression of several important proteins in the mouse striatum after\r treatment with low and non-toxic dosages of AMPH for a short period (mimicking the\r common usage pattern of humans). C57BL6 mice were daily IP-injected with various doses\r of AMPH (0 to 6 mg/kg) for one week. Expression levels of adenosine receptor A2A-R,\r adenyl cyclase type 5,caspase-8, PARP, NF-κB and heme oxygenase-1 (HO-1) in the\r striatum were analyzed by Western blotting technique. Most proteins examined were not\r affected by the 1-week AMPH treatment, except HO-1. A slight but significant increase of\r HO-1 by AMPH treatment indicated that AMPH may cause oxidative damage in brain.\r These results suggest that the injury induced by long-term AMPH exposure warrants our\r further concerns and investigation.
稀子蕨的生殖策略探討
稀子蕨（Monachosorum henryi Christ）生長在台灣中海拔山區，是少數具有特殊生殖方式(不定芽)的蕨類。本研究對東眼山的稀子蕨族群進行物候調查，以了解其進行孢子繁殖及不定芽繁殖的過程，並試圖探討稀子蕨的不定芽是否可增加其族群對環境的適應性。研究結果顯示稀子蕨的孢子體及原葉體都無法在乾旱的環境下生存，常有大規模乾死的現象；而其不定芽則具有很強的耐旱性，無論是在季節普遍性及幼苖發育程度上，生殖芽都比孢子繁殖較佔優勢。而且其不定芽於旱季結束後，可迅速萌發，長出的孢子葉可隨之進行有性(孢子)及無性(不定芽)生殖，使其族群不至於在旱季中有地區性滅絕之虞。;Monachosorum henryi Christ , which exists in the middle elevations of the mountainous regions of Taiwan, is a fern with a special reproductive system seldom found in other ferns.This study investigates the phenology of Monachosorum henryi population in the Don Yang mountain region. Its purpose is to understand the sexual and asexual reproductive cycles of these ferns and to interpret whether or not the buds can increase the fitness of their population during the dry season.The results show that it is extremely difficult for the sporophyte and prothallus of Monachosorum henryi to survive in a drought. However, the buds have a much stronger drought endurance. According to this investigation, the adventitious buds of Monachosorum henryi are superior to the spores in seedling development in every season. Adventitious buds are able to germinate soon after the dry season as well as in any other season, and are able to grow spores and buds on their fronds enabling both a sexual and asexual way of proliferation. In this way the fern avoids a district extinction of their population.
滿足
之M點是否為重心之探索
滿足之M 點，我們稱之為Pi(i=1…n)的均值點。當n=3，M 恰為△P1P2P3 的重心 (G); n=4 時，M 亦為三角錐P1P2P3P4 的重心！因此不免引人遐思：滿足之M 點是否皆為其重心？
我們藉由電腦幾何作圖軟體GSP 協助觀察，掌握了圖形變化間之不變性，再配合向量解析及推理，得以發現均值點、多邊形的重心、以至多面體的重心、及平行多邊形的一般性作法。附帶又發現：任意相鄰三頂點即可決定一平行n 邊形。並進而證實：平行四邊形為四邊形M＝G 的充要條件。但當n≧5 時，平行n 邊形只是n 邊形M＝G 的充分非必要條件！一般而言，具有對稱中心O 的n 個點所構成的圖形必可使M 與G 重合於O 點上。
The point M satisfying is called “the mean point of Pi(i=1…n)”. As n=3, M is the center of gravity (G) of the △P1P2P3. If n=4, then M is also the center of gravity of the triangular pyramid P1P2P3P4. Therefore, I began to wonder if the following assumption stands: The point M that satisfies is always a center of gravity.
By using the computer software GSP (The Geometer’s Sketchpad) to observe figures. It is found that when a figure is changing there is still constancy. Furthermore, supported by the analysis based on vectors, general constructions can be established concerning the mean point, the center of gravity of polygon, the center of gravity of polyhedron, and the parallel polygon. Also, I find that any three neighboring vertexes decide a parallel polygon. And thus it is verified that the parallelogram is the sufficient and necessary condition for quadrilateral M=G. As n≧5, the parallel n-sides shape is the sufficient, not necessary condition, for n-sides shape M=G. In general, a central figure of n points having the center of symmetry O can make M and G meet on O.
這裡真安靜-隔音材質的探討
本實驗針對隔音材質的特性，如各孔板之孔徑、開孔率，並以夾層做不同孔板配置進行研究。本主題共進行三階段的實驗。第一階段探討不同材質的影響，因材質加工問題，實驗誤差過大；第二階段改以PP 塑膠板探討，因儀器誤差，數據難以解析；第三階段仍以PP 塑膠板探討，並修正實驗步驟，以降低實驗誤差。本報告乃以第三階段實驗結果做探討。為了提高實驗準確度，將整個實驗分成若干組，在實驗前後以空白測試，以減低實驗誤差。利用Excel 軟體，進行各組實驗數據噪音傳送損失之修正與分析。本試驗以125Hz、250Hz、500Hz、1000Hz、2000Hz 及4000Hz 六段週波頻率做測試。由分析結果顯示，孔徑與開孔率、同心圓的排列方式，對噪音傳送損失有顯著的影響。;This experiment is to focus on the properties of sound barriers, such as hole diameter, open areas, and the layout of holing boards. We have performed experiments in three steps. In the first step, we discussed the differences between different kinds of material but found many errors caused from faults in the process of making boards. So in the second step, we chose the ploy-propene board but still found errors from instruments. And in the final step, we used the ploy-propene board again and modified the experiment procedure to lower the error from instruments. The report is based on the final step data. With a view to raise the precision of the experiment, we divided the experiment into several parts with the blank test. We modified and transferred the original data to the noisy transfer loss (TL) in the same intensity level, and analyzed the data with Microsoft Excel. In experiment, we detected the noise-pollution level (dB) in the frequency of 125Hz, 250Hz, 500Hz, 1000Hz, 2000Hz and 4000Hz. According to the result, the hole diameter, open area and the layout of concentric circle have a significant influence on TL.
台灣地區青少年體表面積與相關生活因子之研究
人體表面積在醫學的應用相當重要：燒燙傷的評估是以全身面積被灼傷的百分比 表示；營養狀況的評估，新陳代謝率也以單位表面積表示之；體液或藥物之需求量也 是以體表面積來決定劑量；然而人體是一不規則物體，應用一般幾何面積計算公式有 其困難處，如何快速的計算人體表面積，以作為醫療的指引，有其必要性。而青少年 正處於快速發育期，各部位的成長是否會影響表面積的計算，由於目前鮮少對青少年 之專文報告，尤其缺乏台灣地區之調查。為了探索這些問題，乃進行調查與研究。 本研究以台灣地區國民中小學10 至15 歲青少年為對象，探討在此發育期間體格 之變化及可能之影響相關因子，並建立體表面積之快速計算公式。本研究隨機取樣以 1209 人形成樣本，其中男生623 人，女生586 人，利用尺秤，取得身體各部位的資料， 並以問卷調查運動、飲食與睡眠等問題，以探討影響此成長期發育之因子。結果發現： 台灣青少年體表面積快速計算公式為(身高x 體重 ÷37)0.5；其體表面積九分法計算方 式也有別於一般歐美成年人的計算法；及此年齡層的身高與體重受運動的頻率、運動 持久性、飲食習慣多寡的影響，而與運動種類及主食種類相關性不大，這項研究的發 現，將有助於醫護人員對青少年問題的處理。Body Surface Area (BSA) has been used in many clinical conditions to calculate the percentage of burned area, to evaluate the nutrition status - the unit of the metabolic rate, to determine the need of fluid supply or the medicine dosage requirement. So precise measurement of BSA is very important, however the human body is an irregular shape, a laborious task using the geometrical method. To establish a simple quick formula to guide the therapeutic treatment is a necessity. Also the rapid growth phase during the adolescent stage might change the BSA in some way. BSA has not been established for the teenagers in Taiwan. To investigate this issue, a total of 1209 healthy elementary and junior high school boys (623) and girls (586) aged 10 to 15 in Taiwan were recruited by random selection. By use of anthropometrical measurements and a health questionnaire to the subject simultaneously, the data was analyzed statistically. The results revealed that a quick adequate formula derived from the body height and weight for Taiwan teenagers was determined by the formula, BSA = [ Height (meter ) x Weight (Kg) ÷37 ] 0.5, the Taiwan teenage “rule of the nine” of BSA is different from that of the adult, and that the frequency and the duration of exercise, the diet habit, and the duration of sleep significantly influence both body growth and weight. These findings may provide significant references for the physicians to treat the clinical conditions of teenagers in Taiwan.
趨光性及族群壓力的探討
The purpose of the research was to find the relationship between the fruit fly’s attraction to light (or heliotaxis) and their genes. Fruit flies, because of their short life span of approximately two weeks, and their simple requirements for survival, are ideal candidates for the study. With a specially designed device "Mi Gong" for the experiments, fruit flies could be separated and cultivated in accordance to their preference to specific wavelengths of light. They received cross-breeding and were studied to learn the ratio of the resulting offspring in their preference to the light. It was observed that the majority of the fruit flies were more attracted to violet light. It was also found that the next generation of the fruit fly inherited higher sensitivity to the light than their parents. Knowing that there could be potential margin of errors in the experiments, the results of the study demonstrated that light, as an external source, had limited impact to heliotaxis of fruit fly. The study suggested that insects with heliotaxis, including fruit fly, inherited heliotaxis in their genes. The study also pointed out the potential benefits of employing heliotaxis in many areas especially in the agricultural development. Furthermore, heliotaxis can be utilized to study the difference in the behavior of nightlife insects before and after the invention of manmade light source.這項研究，主要是在探討果蠅的趨光性和遺傳的關係。很多種昆蟲都具備趨光性，我們之所以以果蠅作實驗，主要是因為其生活週期短，大約兩週，且易於培養。實驗內容是以「迷宮器材」來鑑別果蠅對某一特殊色光的偏好，將該群果蠅分離出來培養，令其繁衍後代，觀察其後代對此一色光偏好的比率，我們所用的果蠅大致上對綠色光較敏感，而其子代的敏感度較親代高。因此，我們推論趨光性會遺傳，且受光影響，但並非全由光影響，故這可能是實驗中的誤差成因。雖然此實驗是以果蠅為對象，但亦可假設其它具趨光性的昆蟲，也可能是因遺傳而導致其子代有趨光性，而我們可利用其趨光的一些特性，減少農作物因害蟲類的果蠅而損失，並且希望可以得知,在人造光源還未出現在世上時，夜行性昆蟲是否有差異。
極速骨牌-骨牌終端速度及鏈鎖反應機制之探討
本研究主要在探討骨牌脈波在傳遞時的速度變化，並比較在不同的骨牌和不同的排列方式下骨牌的終端速度有何種差異；同時也研究骨牌在鏈鎖反應下能量的放大現象。觀察後發現單列骨牌脈波在傳遞一段距離後，由於空氣阻力的影響，脈波將會達到一終端速度，此終端速度與骨牌高度成反比，而與骨牌質量平方成正比。骨牌的脈波傳遞在鏈鎖反應下仍有一終端速度，但大於單列之骨牌脈波速，且鏈鎖反應具有放大推力之功能。由我們的研究可預測一列物體傾倒時所花費時間和所能達到之終端速度，而鏈鎖反應可比擬為一雷射模型能量集中和釋放的機制，相信可利用骨牌儲存能量的機制應用於需迅速釋能的機械中 This research is mainly discussing the changing of velocity of a domino pulse, and comparing the terminal velocity of various kinds of dominos and arresting modules. Also we focus on the energy-enlarging fact of chain-reaction of domino series. We found that after running a distance, the pulse of a single-series domino will finally reach a terminal velocity by the friction force of air. The terminal velocity will inversely proportion to the height of a single domino, and will proportion to the square of mass of a single domino. During a chain-reaction, the pulse still has a terminal velocity, but it is higher than the terminal velocity of a single series domino .The chain-reaction has an ability to enlarge the original force, too. By the research, we are able to predict the time interval and the terminal velocity while a series of objects are falling. On the other hand, the chain reaction is similar with mechanism of energy concentration and emission of LASER. We also believe that this mechanism is able to explain and apply to those machines which need to release energy rapidly.