臺灣

我們的研究報告，是對校園中所種植的各種變葉木所做的一個研究，經過一連串的實驗證明後，我們確信花青素對變葉木的光合作用會有所影響。接著，我們測定出未氧化的植物色素與已氧化的植物色素吸光能力有很大的差異，我們假設花青素可以吸收某些特定波長的光以防止植物色素的氧化程度過強，實驗後證明我們的假設是正確的。另一方面，我們預期花青素具有保溫的機制，故設計了一個在低溫下花青素可保溫的實驗以證明之，結果和我們的假設相符合。我們預期花青素可利用保溫的特性降低植物因低溫所造成的傷害，減少農業上的損失。This study is about the Codiaeum variegatum which is grown on campus. After a series of experiments, it was proved that “anthocyanin” has a significant influence on the photosynthesis processing in Codiaeum variegatum. A great difference in the pigment of plant’s light-absorbing ability between the oxidized plants and the non-oxidized ones was also found in the experiments. Therefore, it was supposed that anthocyanin could absorb some special range of wavelength to avoid the pigment of plant to over-oxidize. The result of this experiment is in accordance with our supposition. In addition, we anticipated that anthocyanin has the ability to stay warm. By a designed experiment we successfully found that the result is exactly the same as our assumption. According to the findings of our study, we expect the characteristic -- ”staying warm” of anthocyanin could be applicable to decrease the harm to plants caused by the low temperature, and thereby to reduce the loss in agriculture.

傳統的畢氏定理三元二次不定方程x² + y² = z²有一組漂亮的整數解為(m² - n²、2mn、m² + n² )；中國數學家嚴鎮軍、盛立人所著的從勾股定理談起一書中記載四元二次不定方程x² + y² + z² = w²的整數解為(mn、m² + mn、mn + n²、m²+ mn + n² )，這組解被我們發現有多處遺漏，本文以擴展的畢氏定理做基礎修正了他的整數解公式，並推廣取得N 元二次不定方程的整數解公式。 There is a beautiful integer solution formula for the Pythagorean theorem equation, x² + y² = z² , such as (m² - n² , 2mn ,m² + n² ). The “m＂ and “n＂ of the solution formula are integer number. A book written by two Chinese mathematicians, Yen Chen-chun and Sheng Li-jen who expanded the Pythagorean theorem equation to the four variables squares’ indeterminate equation, x² + y² + z² = w² . They claimed that they found its integer solution formula, such as (mn , m² + mn , mn + n² , m² + mn + n² ) for any integer “m＂ and “n＂. But we found it losses many solutions. This paper corrected their faults due to the expanded Pythagorean theorem built by ourselves. Further more, we derived a general formula of N variables squares’ indeterminate equation. Now, we can get integer solutions of the equation, (for all natural number “n＂) easily by choosing integers m1 , m2 , m3 ,……, mn−1 up to you.

This research is mainly in observation with Caenorhabditis elegans ’s genetic mutation caused via nervous system abnormal character. In the study, I the sample have been cultivated purified and add some chemical material EMS to speed up C.elegans mutation. Then based on the character to further analysis what causeof gene deal with mutation and observe the effects in heredity. The research has two stages, on the first stage of study the mainly target is to both search and purify the mutation of C.elegans. The second stage is based on the exploration of mutation’s searching andpurifying. Because the certain mutation bodies aren’t easy to find out, the project is still on progress at the beginning of second stage, and we conclude some heredity special cases in preliminary of study. 這個實驗主要是觀察並針對線蟲因為基因的突變所產生的神經系統異常的變異性狀，在實驗中我先將樣品線蟲培養並純化至一定數量，並加入適當藥劑EMS造成其突變，經篩選並分析此性狀，進而找出造成其突變之基因，以及觀察此性狀對遺傳表現所造成的影響。 該計畫分成兩階段，第一階段的實驗重點是在突變株的搜尋以及純化上，第二階段則是在突變基因的探討上，由於特定突變株的搜尋並非容易，所以目前計畫只進展至第二階段的遺傳實驗初期，對於其遺傳特徵與突變形式上已有了初步的分析，但尚未定位出該基因的位置。

三角形的邊上取任意多個點，我們可以把這塊大三角形沿著切割線切割成較小塊的三角形，但切割線必須是點（或頂點）和點的連線，而且必須切割三角形，同時可以切任意大小的三角形，如圖（1）與圖（2）。但不可以一開始就取走整個三角形。定義拿到最後一塊三角形的人獲勝，而在多邊型中的玩法與在三角形中相同。 我們分A、B、C三種規則來討論，其中A規則即是上面提到的玩法，B規則大部分的玩法和A規則都相同，唯一不同的地方在於：A規則中，只要有一方取到剩下的圖形為三角形，另一方就可以直接取走剩下的三角形，而B規則規定即使剩下的圖形已經是三角形，也必須取到剩下的圖形邊上都沒有分點為止。C規則是限制玩家一次所能取的三角形數來進行遊戲。 我們完成了A、B、C規則中三角形與多邊形的必勝策略，並找出必勝策略之間的關聯。 ;Given any numbers of points on the sides of a triangle, the players can cut this triangle into pieces. Each cutting line has to be one, linked between two points given from two different sides. And the player can’t have to cut smaller triangles out of the original triangle. The out-cut triangles can be chosen randomly without any restriction in size, just like what’s shown in picture（1）and（2）. Meanwhile the first player can’t cut the original triangle exactly all out in the very beginning process. We define the player as the winner, who gets the last triangle. And the above way we play can be applies to any multi-side shapes. We discussed the question respectively in three rules, A, B, and C. Rule A is what we mention above. Rule B is generally the same as rule A, except for the only difference：The rule A , if there is any triangle left , the next player can get it directly, but while in rule B, the every next player has to cut out smaller triangles until no point is left on sides. Rule C proceeds on conditions that there is a limitation to a certain number of triangles cut out at a time. We has finished the winning tactic respectively in rule A, B, and C in the games with a triangle and multi-side shapes. Furthermore, we find the connection between the winning tactives.

Mirabilis Jalapa is a wild flower, which is often seen in countryside of Taiwan. This plant blossom regularly every day around PM 3:00-6:00. Since its regular behavior, it has the potential to become a model plant for research on circadian ryhtem. According to the on spot observation, a Mirabilis Jalapa will bloom consistently, whereas a minority of flower will bloom earlier or later. First, we observe how Mirabilis Jalapa response to disparate environmental conditions. Under a short period of light(8h) and an average period of light(12), Mirabilis Jalapa acts as normal. But under a long period of light, it flowers approximately 1h ahead of time. When under a continuous light, Mirabilis Jalapa shows a regular flowering in the first four day, and after that, circadian rythem of flowering terminate. The ripe flower buds mentain unbloom for 10 days or more, finally end up withered. Meanwhile, floral meristems are also suppressed. Temperature alter seems affct the flowering slightly. Second, we use SDS-page to detect protein divergence 6h interval.But as many of the earlier attempt, the floral stimuli is not sensible for average protein qualitative analysis. So we decide to take more direct approch by genetic experiment. From supplemental material of article” Orchestrated Transcription of Key Pathways in Arabidopsis by the Circadian” we obtain a group of genes regulared by bioclock in Arabidopsis.With Bio Informatics we choose 41 single gene, and compare with sequences in other species, designing promotors to isolate similar genes in Mirabilis Jalapa. Use rt-PCR to detect the level of certain gene expression,and compare characters of those genes in Mirabilis Jalapa with those genes in Arabidopsis. We also blast those 453 genes to the database of animal, trying to recognize some genes that is widely separated between disparat species. And test these genes in Mirabilis Jalapa to confirm this result.本實驗先針對紫茉莉開花生物時鐘的特性進行觀察，並以不同的變因測試對紫茉莉開花時鐘的影響，紫茉莉個別花朵開花生物時鐘並不一致，長日照會對植株造成開花時間提早（約1 小時）的影響，全日照則會對花芽分生及開花行為造成抑制，溫度對於開花影響不明顯。而後利用蛋白質電泳對不同時間點的樣本進行分析，由於開花激素存量極微，故並電泳結果無明顯差異。再來以阿拉伯芥已知與生物時鐘有關的基因中經過生物資訊（Bio Informatics）預測在紫茉莉中存在與開花及光週期有關之基因（CAA75629 CAB56039 AAB60305 AAC49807 AAA82068），針對該基因進行表現量的測定，驗證該基因與開花生物時鐘的關聯性。針對動物界與植物界中已知與生物時鐘相關的基因進行交叉比對，希望找出跨界廣泛存在的生物時鐘基因，接著測試紫茉莉中該基因的存在與否及表現狀況與其他物種的差異，驗證該基因分布的廣泛性。

We understood the definition and meaning of spider number by reading〝Wonders of Numbers〞. It interested us so much. So, we took further step to study the situation of extreme value when the gap sometimes lie on the line and sometimes on the circle or even on both. That is to say, we explored the relation between spider number and the gap when the spider number is maximum or minimum. New research for the application of spider number involves several directions. First, we design a new game called〝Stepping Land Mine〞with the rule of spider number. Give you a net with several hidden gaps, trying to find the right positions of gaps. Second is the further result for a different type of net about regular n-polygon. Third is a tactic for a net with destroying of the strategy points. In this situation, the gaps amount on the circle and on the line are fixed. At the same time, consider the situation of circles and lines designing the tactic of placing the gaps to attain the maximum of the destructive effect. 在本文中我們定義一個蜘蛛網上的蜘蛛數，若在蜘蛛網中加入缺口後，會影響蜘蛛數的大小。我們探討蜘蛛網上的缺口，該如何分配才能夠得到蜘蛛數的極值(最大值及最小值)。先觀察一直線和圓上缺口如何放置蜘蛛數有極值，再探討許多條直線及圓上的情況，進而推展至許多同心圓及通過圓心的許多條放射線的缺口，該如何放置，蜘蛛數才會有極值發生。

有一次上實驗課時看到鄰桌的同學正以實驗室的毛細管吸吮一瓶\r 葡萄汁，每當他吞嚥時，毛細管內殘餘的葡萄汁竟然以近似等速的狀\r 態降回果汁瓶裡，這似乎違背了重力加速度的常理，是毛細管的影響\r 嗎？還是葡萄汁特有的現象？這與毛細管插入葡萄汁的深度有關嗎？\r 這一連串的問題皆因升學壓力而無暇深究。\r 升上高中的那年暑假，我參加了學校舉辦的資優科學營，在物理\r 實驗課中恰好遇到了以毛細管測量液體黏度的實驗，使我有機會深入\r 思索毛細管內液體流速的問題。這個實驗很不好做，要調整兩個定高\r 容器，使水平毛細管兩端產生固定的壓差，讓流經管內的液體為等速\r 的流動。大家手忙腳亂地操作了近三小時，測出來的黏度不僅和老師\r 公布的答案差距甚大，而且各組同學所測得之結果也大相逕庭，不過\r 我們都體驗到了液體黏度對流速的影響。\r 實驗的誤差為什麼那麼大？扣除人為操作誤差後儀器本身還有多\r 大改進空間？有否更精簡的方法測量黏度？毛細管中液體的流速真\r 是固定的嗎？把毛細管斜置或是垂直架置，流速還會固定嗎？重力不\r 會影響流速嗎？若流速真為固定的，如何控制或改變流速呢？是否可\r 以利用流速來測出液體黏度？\r 由於我對這個實驗的專注，在學校選修的專題課程中即以此為題\r 目做長期的研究，在老師的指導下，我和同組同學不停地查閱有關書\r 籍及整理資料，漸漸研究清楚原理後定出實驗計畫，並開始購買材料\r 與工具，長期地動手實驗及改進，兩年來我們利用毛細管中液體的等\r 速及不等速流動的特性，發展出了兩種既精簡又準確的液體黏度測量\r 法，以下就是整個研究及創作的過程。\r \r \r The viscosity is one of the most important parameters of the fluids. In conventional viscosity experiments, capillary-based viscometers are widely adopted because of their user-ready devices and moderate prices. However, to accurately measure the viscosity, the fluid velocity must be kept constant; otherwise, the fluctuation may cause the serious deviation. Besides, traditional capillary viscometers often require a long time to make the measurement. This research aims at exploring the capillary fluid mechanics and developing accurate and rapid methods to measure the viscosity. In this study, we developed two creative viscosity-measuring methods, the gravity sloping helical structure and the gradational liquid-level difference, and constructed two cost-effective capillary viscometer prototypes accordingly. The gravity sloping helical structure employs a long helical capillary as the flow channel and utilizes the gravity force to keep the fluid velocity extremely constant. The highlight of this method is that we can see the fluid flow through the capillary directly. On the other hand, the gradational liquid-level difference method uses the pressure sensors to precisely monitor the liquid-level difference, which drives the flow in the capillary, and allows automatic measurement of viscosity. Compared with computer simulation, the experimental results agreed well with the theoretical values. The gravity sloping helical and gradational liquid-level difference methods achieve 0.5% and 0.8% accuracy respectively. In addition, the automation of viscosity sensing also greatly facilitates the viscosity measurement. Furthermore, these two methods are both valuable for incorporating into educational purpose and industrial application.

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.

奈米的科學與技術將是21 世紀所要探討的方向。在了解奈米粒子的表面效應、小尺寸效應、量子尺寸效應、宏觀量子隧道效應後，發現其應用甚廣，諸如再生物、醫學、環境、國防、工業產品等方面，都將佔有很重要的地位。我們主要是利用溶膠-凝膠法來製造二氧化鈦奈米粒子，並了解二氧化鈦奈米粒子可吸收紫外線及光催化反應，將廣泛應用電子、紡織、塑膠、橡膠，空氣淨化及廢水處理方面。本實驗將利用二氧化鈦的吸收紫外線特性，來研究其應用在化妝品上面。The science and technology of nanomater will be the direction we will explore in the 21st century. After understanding surface area effect of nanometer particle, Small size effect, Quantum effect, and Macroscopic quantum tunnel effect, we can diswver the application is very far-fluing. For example:biochemistry, medical science,eneironment,national defense and industrial products,will devine a very important position.We mainly use sol-gel method to produce U-TiO?,and understand the absorption of UV and photocatalysis,plastics,mbber,purging air,and dealing with effluents.This experiment will use characteristic of absorbing UV of U-TiO? for researching the application of cosmstics.

秀麗隱桿線蟲(Caenorhabditis elegans)為在科學界備受矚目的模式生物，對於其生殖及發育過程已有諸多研究，然而對於其覓食及攝食行為的相關研究卻仍闕如；每一種生物都有其獨特的行為模式，而為了解線蟲發展出何種覓食與攝食的行為以適應自然的環境，因此著手進行研究。本研究歸納出線蟲的七種一般行為：前進、探頭、偏移、擺頭、後退、轉向及拐彎行為，並探討其意義。其中，前進及探頭行為為恆常出現。偏移與轉向行為與攝食有關，在有菌環境中出現，可避免其遠離食物來源，而連續的後退及轉向行為也構成特殊行為之樹枝狀行為，推測應為幫助線蟲的消化所出現的行為。擺頭與拐彎行為與覓食有關，在無菌環境中出現。後退行為雖在有無菌環境中皆出現，但由後退後行為的不同可以了解後退行為在兩種環境下具有不同意義。在有菌環境中，後退後通常伴隨轉向行為；在無菌環境中，後退後通常伴隨拐彎行為，為逃離不適環境且藉以覓食的行為。經過研究，發現線蟲的覓食機制為嗅覺，且對嗅覺有依賴性及專一性，在其他氣味存在的環境下會大大降低覓食的效率，但最後仍然能正確地找到食物來源。線蟲於覓食的過程中所出現的特殊行為之混亂行為，由實驗結果發現為是E. coli 所釋放至培養基的化學物質所造成，化學物質濃度越濃，線蟲所表現出的混亂行為就越明顯。推測此種現象發生的原因，應為E. coli 釋放化學物質以干擾線蟲，以避免本身受到捕食，然而，線蟲也演化出適應的能力，因此在發生混亂行為後仍然能抵達菌落，此種特殊的交互作用表現出線蟲與E. coli 間的共演化現象。Cenorhabditis elegans has long been a model organism used for developmental biology studies. However, researches about its foraging and feeding behaviors are still limited. Every organism has its unique behaviors, and this research was conducted in order to understand more on what kind of foraging and feeding behaviors were developed by C. elegans and how they helped C. elegans to adapt to the environment in which it lives. The research concluded with seven general behaviors of C. elegans : advancing, probing, slanting, swaying, backing, turning and bending, and the meanings of it. The advancing and probing behaviors are constant. The slanting and turning behaviors, which appear in presence of food, are feeding-associated behaviors, which help C. elegans avoid leaving the food source. Continuous backing and turning behaviors also make up the branching behavior, one of the special behaviors, which help C. elegans’ digestion. Swaying and bending behaviors, which appear in absence of food, are foraging-associated behaviors. Although backing behavior appear both in presence and absence of food, the difference in post-backing behaviors show that there are distinct meanings of backing behavior in each environment. In presence of food, turning after backing is usually observed; in absence of food, bending after backing is usually observed, which indicates the act of escaping from unsuitable environment and searching for food. Studies show that the foraging mechanism of C. elegans is by olfaction, and C. elegans is highly olfaction-dependent and specific: efficiency of foraging decreases significantly under environment with scents other than that of E. coli, but C. elegans is still able to locate the food. According the experiments, the chaos behavior, one of the special behaviors, appears during the foraging process of C. elegans, and is caused by chemicals released to the medium by E. coli. The density of the chemicals and the extent of chaos behavior is in direct proportion. The theory is E. coli secrets chemicals to disturb the worm to avoid being preyed upon. C. elegans, however, also evolved the ability to adapt to the chemical so that it can still reaches the food source even after chaos behavior appeared. This unique interaction is a manifestation of co-evolution between C. elegans and E. coli.