2007年

BCH (Bnip-2 and Cdc42GAP homology) domains are a novel class of protein-interacting domains. First identified in BNIP2 and in Cdc42GAP, a GTPaseactivating-protein (GAP), canonical BCH domains play important and varied roles in the control of cell morphology and apoptosis induction, amongst others. However, this domain is currently classified under lipid-interacting sec14 domains due to low sequence identity (~20%). Given this intriguing similarity, the relationship between BCH and sec14 domains is worth further study. As BCH/sec14 domains are closely associated with cell signaling and human disease, characterization of these domains and the elucidation of their functional diversity could better aid our understanding of their cellular functions and disease pathogenesis.

剛開始考慮平分物件時，我們從二維的多邊形部分著手，後來發現已經有人做過相關研究，並且得到類似的結論。這個部份顯現出面積平分線與其包絡曲線間的密切關係。我們將其中的方法和結果加以歸納、改善，為了更全面地研究，我們推導出一般性的包絡方程。之後當我們推廣到三維領域時，發現四面體體積平分面與之前的結論有些相似之處，平分的情況卻也更複雜，我們將推導的結果用電腦軟體呈現出來，以便更深入地了解它。最後嘗試了相當抽象的高維積平分，結果仍具有工整的對稱性，讓我們充分領略了數學之美！When considering bisecting a subject, at first we focused our attention on 2-D case, polygons. But afterwards, we found there were already some similar studies conducted by other students, which indicated the close relation between the area-bisecting lines of a polygon and their envelope. We rearranged their methods and results, and then made further improvement. Moreover, in order to study the bisecting problem entirely, we derived the general envelope equation. Then when extending the generalization to the 3-D case, we came to the conclusion that tetrahedrons’ volume-bisecting planes is similar to that in 2-D, but the circumstances are more complex. We tried to show our result with the aid of software, hoping to understand it fully. Finally, we tried to do the case in higher dimension, which is very abstract, and the result was clear-cut symmetrical. During the studying process, we had seen “the beauty of mathematics.”

搜尋太陽系外行星（extra-solar planet；exoplanet）是當今天文學家最重要的計畫之ㄧ；其中，當系外行星經過其主恆星碟面時，會造成光度略微下降，稱之為凌日現象（transit） 。本研究便是利用鹿林天文台SLT（Sne Little Telescope）望遠鏡來拍攝兩顆已知的系外行星HD 189733 b 和HD 209458 b在凌日時的影像。 我們得到約4000 張影像，再經過影像修正與資料分析後，我們作出凌日光變曲線圖、Bin圖及相位圖，並從中探討其特性。 經分析判斷後，HD 189733 看到一個剛開始發生和一個完整的凌日現象，分別由B濾鏡和 R 濾鏡所拍攝；而 HD 209458 則看到兩個剛開始發生，三個要結束的凌日現象，分別由B濾鏡、R 濾鏡和 Hα 濾鏡。 並由光變曲線，推得HD 189733 的基本參數，包括：行星半徑為 1.242個木星半徑、軌道傾角為88.94 度以及軌道半徑為 0.03115 天文單位。 Since 1995, more than 200 extra-solar planets have been found. Until today, astronomers still make efforts in searching extra-solar planets because it’s one of the most important projects in this century. During the crossing by the stellar disks (i.e., transits), the exoplanets will cause the brightness to decrease by a small amount. In the project, we have focused on the observations of two known transit exoplanets, HD 189733 b and HD 209458 b. The photometric observations were performed with the 40-cm SLT telescope on the Lulin Observatory. The results from the image procuring, data reduction and analysis are presented. We accrue and plot the light curve, bin and phase. We found out that HD 189733 has two transit ingresses with B, R band, and HD 209458 has two transit ingresses, two transit egresses with B, R, Hα band on phase. We figure out planetary parameters, RP is 1.242 RJ, inclination is 88.94° and orbital semi-major axis is 0.03115 AU by transit light curve.

Starting from the problem in AMC competition of Australia, we try to find out the locus and its length when a point in a regular polygon rolls in a circle. The result is that the locus has a wonderful and regular cycle.Next, we discuss the regularity of the cycle when a regular polygon（n sides） rolls in another regular polygon. Furthermore,we discuss the the equation of the locus by changing the radius and the angle of rolling. we find out the argument function of the locus of a point inside when a a regular polygon（n sides）rolls in another regular polygon （m sides）： ， Aj is the summits of the regular polygon（m sides）, Bjcorresponds Aj when a point inside the regular polygon (n sides) rolls, ) And then, we do some moving simulation with some computer math software, such as Cabri Geometry、Mupad, etc. We discuss the regularity of the locus and its equation of a point inside when some special cycloids, like asteroids, cardioids, etc, roll in a certain condition. Moreover, with the result of research 2, we create the “plate＂ and apply for a patent on it. We hope to study math by playing games. 從澳洲AMC 競賽題出發，嘗試探討一正n 邊形中的一點在單位圓內滾動軌跡及其軌跡長度，發現該軌跡均會產生奇妙的循環規律。 接下來，推廣探討正n 邊形在其他正多邊形中滾動時循環的規律，並利用旋轉半徑及角度之間的變化深入探討其滾動軌跡方程式，發現正n 邊形繞正m 邊形滾動時其內部一點軌跡參數式為，其中， Aj 為 正m 邊形之各頂點、Bj 為正n 邊形中內部一點旋轉時對應 Aj 之點，。 進一步想嘗試使用數學電腦軟體如：Cabri Geometry、Mupad 等對以上研究去做一些動態模擬，並再探討一些特殊擺線如：星狀線、心臟線…等，在條件下相切滾動時，圖中某一點的軌跡規律性及其方程式。另外，應用研究二中的結果，創造出寓數學於遊戲的「圖形板」，並申請了新型專利。

We operated the misexpression screen between the EP lines and the pattern lines with the genotypes of eq1>dll, eq1>abdA, eq1>Ubx, eq1-GAL4, ey-GAL4 or dpp-GAL4. After the screening, we found that five of these 1,800 strains of filial generation had special phenotypes. It had shorter antennae and defects in the anterior equatorial region of eyes. We used plasmid rescue and IPCR to sequence the certain target gene, and found that it was escargot, abbreviated as esg. To identify when, where and how the overexpression of escargot induces such phenotype, we operated the staining of eye-antenna disc in third-instar larval period of wild type, eq> esg×UAS-GFP and eq>GFP with anti-dll, anti-caspase3 and anti-esg. The result shows that escargot cannot be detected before puparium formation. But the expression of dll, a gene controls the eye development, was reduced in the eye disc. We except the overexpression cause the defect of distal antennae and the anterior equatorial region of eyes mainly in the 3-day-long pupal life.我們用異位表現法篩選出和eq1>dll、eq1>abdA、eq1>Ubx、eq1-GAL4、ey-GAL4或dpp-GAL4 這些pattern lines有交互作用的EP lines。在這1800種的果蠅子代品系中，有五種具有特殊的性 狀。它們具有觸角短化以及複眼前緣中央區有缺刻的現象(形成心型眼)。我們使用質體救援 法以及IPCR的方法來定序這段未知基因序列，發現這是一個叫做escargot的基因(簡稱esg)。 為了了解過分表現此基因會造成何種分子影響，以至於產生此種性狀，因此我們使用 anti-dll 、anti-caspase3 和anti-esg 進行野生型、eq>esg×UAS-GFP 和eq>GFP 三齡幼蟲的 eye-antenna disc的螢光免疫染色。結果在幼蟲成蛹前都沒有偵測到esg的表現現象；不過在eye disc中，控制眼睛發育的基因dll的表現有被抑制的現象。因此我們推測過分表現esg的過程因 該是發生在為其短短三天的蛹期。也就是說，這種表型應該是在化蛹後形成。

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.

本文所探討的議題為電解質溶滿通以電流後所產生的效應與機制。本實驗所採用的方法為電解與電鍍，運用這兩種方法，來比較電解液在不同狀況下所產生的結果；經過多次的實驗，累積了許多實驗結果，使我們可以得到更精確的數據 · 在此次實驗中，我們發現電解液在相同的電壓下，通以電流後的穩定性與金屬的活性有關，活性越大越不穩定；反之，活性越小越穩定。另一個發現為，只有單一極性離子移動的情形，可通過的電流，比陰陽離 r 同時移動時為大；但因通過的電流大使電解液反應劇烈，產物時時覆蓋電極使電流下降。所以就穩定性來說，是以陰陽離子同時移動為佳 · 在展望方面，希望可以發展到液態磁屏避的設備，可減少設備過重之問題 ·This is a study of how electric current effects the electrolyte solution. The experiment was conducted through two methods: electrolysis and electroplating, the results of which were compared. The experiment of the same designs hi been conducted repeatedly and, as a result, accurate data were collected and accumulated.One of the two major findings from the experiments was that, when under the same voltage, stability of the electric current varied with the change of activity of the metals; the greater the activity of the metals, the less stability of the current, and vice versa. The other major finding was that, with the movement of dipole-ion, a greater amount of current would go through the solution than that which would go through with the movement of cathode and anode; however, the greater amount of current would cause intense reaction of electrolyte solution, hence merging the electrode and reducing the current. So as long as stability is concerned, the movement of cathode and anode is preferable.It is hoped that more sophisticated experiments designed on the basis of the similar principles will eventually lead to the construction of equipment of liquid-magnetic shielding of smaller weight and size.

能源危機日益嚴重，開發再生能源成為當務之急。在諸多的再生能源之中，太陽能最易於使用，且可源源不絕的不斷取得利用。但目前太陽能電池的效率始終不高。其中重要的原因是太陽本身的頻譜多為短波長，並不適合絕大部分頻譜響應較佳，多為長波長的太陽能電池。目前改善效率方式，多為改變太陽能電池的頻譜響應以配合太陽之頻譜。本研究提出反向思考的概念，藉由頻譜轉換的方法，改變照射在太陽能電池上的太陽光頻譜，以提升太陽能電池的效率。本研究利用一種珊瑚礁的螢光蛋白質（DsRed）以及人工合成的螢光染料（Cy-5）最為本研究的頻譜轉換的材料，加於低成本，目前市場佔有率較大的單晶矽太陽能電池上，經由理論與實驗的結果顯示，增加的發電效率約為3~5%，證實利用頻譜轉換的概念確實可以提升太陽能電池的效率。Energy crisis has become more and more serious in recent years, which makes recycled-energy development is a must. Among different recycled energies, solar power has two advantages, that is, easy-to-use and endless supply. However, the conventional solar cell makes poor use of the solar spectrum because the solar spectrum is mainly composed of short-wavelength, which can’t fit to most of solar cells which is more sensitive to long-wavelength. Currently, the major method to improve the efficiency is change the function of spectral response, such as concentration lens, tracking devices, and antireflection coating. Up to now, no one notices the possibility of changing solar spectrum yet. This research provides an insight into this issue. Instead of changing the function of spectral response, I changed the solar spectrum, which irradiates solar cells through spectrum conversion to improve solar cells’ efficiency. This research uses one kind of coral fluorescence proteins (DsRed) and one kind of artificial fluorescence dyes (Cy-5) as the materials of spectrum conversion. Then coat them on the low-cost and high-market-share mono-crystal-Si. According to the theories I researched and my experiments, the improvement of the efficiency is about 3~5%, which proves it is actually useful to elevate the efficiency of solar cells through spectrum conversion.

The reason for making this project was with the intention to help the blind persons. A lot of people with vision problems don’t have the resources available to acquire equipment or programs that make it easier for them to use a computer to write, to communicate etc... Being aware of this problem we took the liberty of researching at a community center that helps the blind persons in Tijuana Baja California, Mexico. We found that they had a type writer (Perkins) with only 6 keys that symbolized Braille. They also had a normal keyboard that had the Braille code over each key, but it is complicated to learn because of its many keys. Due to our research our intention was to design a system that respect the Braille symbols of the Perkins type writer and translated them to the common alphabet. We believe that this project will help many people especially the blind, with writing books, letters, articles, etc. So they can be integrated to activities and jobs reserved, until now, for people with the sight sense. My project also has 8 keys, when the person press a key combination the PC emits the sound of the letter. And when a word is completed the PC reproduce the whole word on the speaker. When the entire paragraph is completed there is an option to reproduce it. It has also other functions as erase everything, back space, etc. All these with the 8 keys. To control the system I used the parallel port of a PC, with a control program made in Visual Basic. Currently there are systems for the blind but are very expensive, they have a cost of approximately $900.00 US dollars, which is a high price to pay for some people. My project has a cost of $70.00 US dollars thus making it easy for a person who has a computer to be able to buy this keyboard. This project is being use in the “Blind Persons Training Center” of Tijuana city. They helped us to develop it, giving some ideas to improve it.

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.