2008年

高斯曾經提出八皇后問題：八個皇后在8 × 8 的棋盤上有幾種放法可以使任意兩皇后不會互相攻擊？我們在原來的問題上加上一些條件，改變皇后攻擊規則，使得皇后失去一條對角線的攻擊方向，稱之為「跛腳皇后」。我們稱一個在棋盤上放置最多跛腳皇后使其不互相攻擊的放法為好放法；研究跛腳皇后放置在各類棋盤上其好放法的個數和性質。我們分別在六種棋盤上做討論：（1） 在平面n x n 棋盤上，我們證明了其好放法與完美極致史考倫型數列之間的對應關係，並歸納出相關的性質和定理。（2） 在平面m x n 棋盤上，我們固定一邊長度n，做出n 較小時好放法數的通式；我們也將其好放法對應至廣義史考倫。（3） 在環面n x n 棋盤上，我們說明了其好放法與完全剩餘系排列之間的對應關係，並歸納出相關的性質和定理。（4） 在環面m x n 棋盤上，我們固定gcd（m,n），做出gcd（m,n）較小時好放法數的通式。（5） 在柱面n x n 棋盤上，我們證明其與環面n x n 棋盤等價，說明其好放法具有和環面n x n 棋盤好放法相同的性質和定理。（6） 在柱面m x n 棋盤上，分成左右柱面以及上下柱面來做討論。我們歸納出相關性質和定理；並固定一邊長度n，做出n 較小時好放法數的通式。Gauss had researched about putting eight queens on the chessboard on the way that doesn’t make any queen attacks another one. Thus, we added some rules on the question: the queen loses one diagonal attacking-way and become the “lame queen”. We call a way that doesn’t make any lame queen attacks another one “a good way”. We have been investigating the amount and properties of good ways based on six kinds of chessboard: （1）We found the correspondences between the “good way” on n × n plane chessboard and the Perfect extremal Skolem-type sequence, and concluded some associated properties and theorems. （2） On m× n plane chessboard, we fixed the length n of one side of the chessboard, and accomplished the amount of good ways when n is small. We also correspond the good way to the Generalized Skolem.（3）We found the correspondences between the “good way” on n × n torus chessboard and the arrayal of complete residue system, and concluded some associated properties and theorems.（4）On m× n torus chessboard, we fixed the gcd(m,n) （greatest common divisor of m and n）, and accomplished the amount of good ways when gcd(m,n) is small.（5）On n × n cylinder chessboard, we proved that this kind of chessboard is equal to torus chessboard. So the good ways, characters, and theorems on cylinder chessboard are the same as on the torus one.（6）On m× n cylinder chessboard, we separate it into two cases: left-right cylinder chessboard and up-down cylinder chessboard. We concluded some associated properties and theorems, and we also fixed the length n of one side of the chessboard and accomplished the amount of\r the good ways when n is small.

This work presents fundamental research in the field of algebra and the theory of number. The subject of the work is equations of Markov's type (the type of the equations introduced by me earlier which generalizes the classic equation of Markov (x2+y2+z2=3xyz)) of parabolic type with two unknown quantities and their genealogical trees. The following questions appeared when I was working on the equations of Markov's type and constructing genealogical trees to them: are there any other trees besides one for a certain equation; how to find all the genealogical trees for the equation of Markov's type; how to find all the integer solutions with the help of the genealogical trees. This work is devoted to the analysis of these questions. The aim of the work: to create the method of finding all the integer solutions of the equations of Markov's type of parabolic type. The tasks of the work: 1. Carrying out some experimental works to find all the genealogical trees for a concrete equation. 2. Formulating a hypothesis that the curve has a specific part. 3. Research the parabolic type in order to apply the hypothesis to it. 4. To formulate and prove the theorems about the necessary and sufficient conditions of the existence of the genealogical trees of the integer solutions of equations of Markov's type of parabolic type with two unknown quantities. As the result of the work all the tasks have been solved. I worked the method of finding all the integer solutions: : to find all the integer solutions by means finding all genealogical trees of the equations of Markov's type of parabolic type with two unknown quantities you need : 1. To investigate if there any integer solutions‧ a special part of the parabola (if it is a parabola)‧ a special part of the parallel lines (if it is a pair of the parallel lines) 2. To build a genealogical tree from every solution (if they exist). 3. All the integer solutions will be on the constructed trees. I also worked out a computer program which is based on the usage of this method.

受應力拉伸時，橡膠溫度明顯上升；縮放回原長，橡膠溫度驟降。由文獻得知橡膠內部具有特殊的鍵鍊結構，在一般的情況下，交鏈分子糾結成一團，狀態複雜；受外力拉伸時，交鏈分子依橡膠長度之增加而伸展，排列較為整齊，狀態之複雜度減小。根據熱力學第一定律，當內能變化為零，則外力作功會造成能量變化。在定溫之下，橡膠內能變化為零，當其受應力拉伸，使其內部交鏈分子排列複雜度降低，造成橡膠熵值減小，而有能量（dQ=TdS）的釋出。測量此一能量dQ 變化，即可計算出熵與狀態數之變化The temperature of rubber rises as it is stretched, its temperature comes back again while it restores to its original length. It is known that the rubber is consisted of long-chain molecules, the long-chain molecules strangle each other at normal state, however, they become more order when the rubber is stretched. Based on the 1st law of thermodynamics dU=dQ+dW, The deformation caused by applied force supplies energy to the rubber and reduce its entropy, the heat dQ (=TΔS) released by the reduction of entropy causes the temperature rise of rubber as dU=0. We report the study on the correlation of thermal properties and the molecular network in rubber, from the measurements of temperature change, the changes of entropy and the changes of states’ number were estimated.

This Project is inspired by the situation incurred by pedestrians, which for the most part are students who need a crossway in order to obtain public transportation or to get to the school; the difficulties that are faced by the personnel to exit the parking lot as well as the students who have a vehicle and to help those parents who drop and pick up their children at the school. At the same time, we would like to reduce the amount of contaminated gas emissions that are emanated into our environment. As consequence of the emission of toxic substances, the air contamination can cause side effects such as the burning of eyes or ears, throat irritation and itching and or respiratory problems. Under determined circumstances, some chemical substances that are found in the contaminated air can produce cancer, congenital malformation, brain damage and disorders to the nervous system, as well as, pulmonary damage and harm to the respiratory tract. For the present investigation it has been suggested as a primary goal: The development of a device, in this case a traffic light, which has the objective to reduce the previously mentioned traffic/security problems that arise upon entering and exiting the institution. The secondary goal is to have a friendly ecological impact within our community. This device was built and tested during a month to obtain figures and demonstrate benefits reported. The device should be low maintenance, it should have a long lifetime and, be simple enough to be operated by those who use it. Among the benefits found, the safety of the students, the prevention of accidents such as: car crashes and run overs, etc. Our studies indicate that per week it is consumed an average of 2,020.16 liters of gasoline, in schedules of 13 hours (from 7:00 AM to 8:00 PM) to lessen this figure would have a good ecological impact since all the hydrocarbon emission are harmful to health.

Hadley has create a system that enables you to see in the dark, night?vision goggles. The military version usually retail for thousands of dollars, but Hadley’s solution costs considerably less. And they really work! He has even attached close?fit rubber swimming fittings to the eyepieces to ensure you can’t see a thing without the help of the electronics. The key feature of this project is the way Hadley has used his imagination to access and modify existing technology and explore ways of ‘hacking’ these device to obtain useful component system that he can integrate to make a fully functioning product. In doing this he has encountered many unsuitable combinations, but has persisted to reach an extraordinarily effective endpoint. The whole process, which has taken over a year from initial idea to result is a demonstration of tenacity and ingenuity.

Adducin蛋白在細胞骨架的調節上扮演著重要的角色。然而，近來有許多研究指出，骨架蛋白也會出現在細胞核並參與轉錄調控，因此本研究的目的即在探討adducin蛋白是否會進入細胞核中，並參與轉錄調控或具有其他功能。在本研究中，我們將綠色螢光蛋白(GFP)標示的adducin質體DNA，利用轉染技術送入老鼠纖維母細胞株NIH3T3中表現。NIH3T3細胞原本並無adducin蛋白的表現，在共軛焦顯微鏡下觀察，野生型的GFP-adducin蛋白會表現於細胞核與細胞質中。由於adducin蛋白尾端序列攜有可能往核內運輸的訊號，於是將位在此一訊號中的離胺酸718及離胺酸719進行突變，結果發現此一突變株只能在細胞質中表現。此外，蛋白磷酸脢C(protein kinase C)已知能磷酸化adducin蛋白在絲胺酸716及絲胺酸726的位置，於是假設其磷酸化是否與其在細胞內的分布有關。將adducin的絲胺酸726置換成丙胺酸，並不影響其在細胞內的分布。然而將絲胺酸716置換成丙胺酸後，則完全只在細胞核中表現。由於adducin可分布於細胞核，因此我們懷疑adducin蛋白可能與細胞分裂有關，於是本研究利用流式細胞儀分析adducin轉染後NIH3T3細胞的細胞週期。流式細胞儀的分析結果顯示，攜有GFP-adducin或其突變株的細胞與未經轉染的NIH3T3細胞的細胞週期並沒有顯著差異。其次，為了避免因轉染的效率不高而造成統計上的誤差，我們利用顯微鏡追蹤技術觀察攜有GFP-adducin的細胞株，結果顯示攜有adducin突變株的NIH3T3細胞株仍能正常分裂。再者，因為adducin能與細胞骨架中的肌動蛋白結合，所以adducin不同的分布位置可能影響細胞附著與細胞展延的效率。細胞展延試驗的結果顯示，adducin及其突變株對細胞附著與細胞展延的效率並無明顯的影響。本研究的結果證明，adducin的確帶有往核內運輸的訊號，其在細胞質中的分布可能也同時受到絲胺酸716磷酸化的影響。然而adducin的功用似乎與纖維母細胞的分裂與展延無明顯的關聯性。Adducin, an actin binding protein, is known to play an important role in the regulation of the membrane cortical cytoskeleton. More and more evidence indicates that proteins involved in the cytoskeletal regulation could also reside in the nucleus and participate in gene regulation. Thus, the goal of this study is to examine whether adducin is expressed in the nucleus and involved in certain nuclear events. In this study, adducin and its various mutants were fused with green fluorescent protein (GFP) and transfected into mouse NIH3T3 fibroblasts which do not have endogenous adducin for monitoring their subcellular distribution under a laser scanning confocal microscope. The wild-type GFP-adducin was found to be present both in the nucleus and in the cytoplasm. The COOH-tail of adducin contains a motif analogous to the nuclear localization signal (NLS). Mutation of two lysine residues (lysine 718 and lysine 719) located within this motif abolished the nuclear localization of adducin. Moreover, adducin is known to be phosphorylated by protein kinase C at serine 716 and 726. Substitution of adducin serine 726 with alanine had no effect on its subcellular localization. In contrast, substitution of adducin serine 716 with alanine led to only nuclear expression. Nuclear localization of adducin renders it possible that adducin may be involved in the regulation of cell division cycle. For cell cycle analysis, flow cytometry was applied. The results of flow cytometry indicated that expression of adducin and its mutants in NIH3T3 fibroblasts did not affect their cell cycle progression. To further examine the effect of adducin on cell division, NIH3T3 cells transiently transfected by adducin were monitored by time lapse video microscopy. The video clearly showed that the cells with GFP-adducin underwent cell division to generate two daughter cells. Since adducin is well known to bind to actin and thereby regulate microfilaments, we wondered that expression of adducin in NIH3T3 cells might affect their adhesion and spreading onto extracellular matrix proteins. The results of cell spreading assays showed that adducin appeared not to affect cell spreading. In conclusion, our results demonstrate that the subcellular distribution of adducin is likely regulated by two signals, one is the nuclear localization signal and the other is the phosphorylation status of the serine 716. However, enforced expression of exogenous adducin in fibroblasts such as NIH3T3 cells does not alter their cell cycle or cell spreading on fibronectin.

本研究是藉由數學手法探討；如何由一疊 36 張四種花色的撲克牌中，尋找出保證可猜中最多張花色的方法。研究過程是以在適當的猜牌時機，以邏輯推理、二進位、分析與歸納 … … 等數學原理與方法，搭配巧妙的策略運用而達到目的。 猜牌方法：先約定好猜牌規則，助手將 36 張牌背圖樣相同但非對稱的撲克牌，以旋轉牌背的方向傳達訊息。在本研究中得出「經由巧妙的猜牌方法保證可以猜中不少於 26 張花色」，並得出「當總張數趨近於無窮大時，保證可以猜中不少於 81 . 07 ％的牌，並且證出若僅使用獨立的訊息猜牌，無論任何猜牌方法皆無法猜中多於 87 . 37 ％的牌」 · 其中一個猜中多於 80 ％的例子是‘「當總張數等於 23006 張時，保證可以猜中不少於 1 8405 張牌（18405/23006 > 4/5）」 ·The study is mathematically based with reasonable explanations behind it. We are to correctly guess as many cards as possible from a deck of 36 cards, with random numbers and four different suits. We will apply mathematical methods, such as logic inference, binary system, and analytical reduction, upon right timing. Using careful arrangement of the principles and reasoning, we can reach our ultimate goal. To state guessing: Conference between the guesser and the assistant about the guessing rules, the assistant will have 36 cards with the same exact pattern on the back but not symmetrical. The pattern of the cards will be different when rotated 180o. The only communication between the two is by rotating cards. In this study, we can prove that through mathematical method, we can assure 26 or more cards can be correctly guessed. Furthermore, when the total amount of cards is close to infinity, we can assure 81.07% or more of the cards can be correctly guessed, and prove that if the cards are guessed from independent information, no more than 87.37% of the cards will be correctly guessed by any guessing methods. One of the examples, which 80% of the cards are correctly guessed, is that when the amount of the cards is 23006, 18405 or more of the cards can be correctly guessed. （18405/23006 > 4/5）

自組薄膜(SAMs, self-assembled monolayers)乃是具有特定官能基的化合物在不需外力作用 下自動吸附到基質表面上而自行排列成有自序規則之結構。SAMs技術因製備容易且穩定，在 應用上深具潛力。目前此方法中，以硫醇接在Au上的研究最為廣泛。本作品希望藉著SAMs 方法將硫醇分子吸附於鐵片或其他金屬表面上，以達成防鏽與抗酸目的。我們分別透過接觸 角量測研究正十二硫醇在鐵片上形成分子薄膜的可能性；利用酸與金屬產生氣體的速率研究 分子薄膜抗酸蝕的情況；測試分子薄膜的耐熱性；根據鐵片生銹時pH值變化、重量變化與[Fe2+] 含量差異來探究分子薄膜能否防鏽；最後找出適合形成分子薄膜的濃度與溫度效應。由實驗 結果我們發現SAMs薄膜確實能吸附於鐵(及鎳、銅、鋅等金屬)的表面上並增加抗酸與防鏽蝕 能力，薄膜對熱的穩定性極佳，35℃時結合效果較佳，而濃度的提高有助於SAMs的效用。 Self-assembled monolayers(SAMs) are elements which have specific functions.SAMs,ordered molecular aggregates can automatically adhere to the surface of substrate without any force.The applcation of SAMs’technique has high potential not only because ther are easy to make but also because they are stable.Exposing molecules such as alkyl thiols to an Au(0) surface is now in widespread use. In this work,we apply the thiols chemisorb onto the Fe or other metal surface to make it rust-resistant and acid-resistant.We study the following issues to find the appropriate conditions of forming monolayers in varying concentration and temperture: I. The possibility of forming n-dodecanthiol molecular monolayers on Fe surface by measuring the contact angles. II. The ability of antiacid corrodibility by comparing the rates of producing gas from acid and metal. III. The heat-resistant of molecular monolayers. IV. Whether it’s antirust by detecting the changes of pH,weight,and the concentrations of Fe2+ during the iron rust. According to the results,we conclude SAMs do adhere to the surface of Fe(and other matal like Ni,Cu,Zn), which increases the ability of antiacid and antirust.Besides they are stable to heat, have good combining effect at 35℃, and it is beneficial to the effect of SAMs through raising their concentration.

The main purpose of this study is to explore whether fruit flies (Drosophila melanogasters which background is 2U) can distinguish and memorize different colors and smells by learning. Futhermore, to find out the relation between age and learning ability, and analyze the influence of repeated training on how long the memory would last. According to our experiment, in smell training, the fruit flies are able to distinguish and memorize different smells, and young fruit flies have better memory than old flies. In color training, the fruit flies can distinguish and memorize different colors, but the effect was less than that of smell training. In intensive learning, proper times of learning increased the memory ability, but excessive learning exhibited an opposite effect. In the labyrinth experiment, we select and nurture the fruit flies having the best color memory in order to further understand the gene correlated with the memory learning. In addition, in one-time training, fruit flies are able to remember the smells and colors in four minutes, and young ones have the better ability. In six-time training, fruit flies have the ability to remember the smells and colors in twelve minutes. In the end, we hope you can know more about the learning and memory ability of fruit flies through our report. 本實驗主要探討果蠅是否可經由學習分辨、記憶顏色與氣味，並探討年齡與學習能力的相關性、分析多次訓練對記憶時間的影響。由實驗結果得知，氣味方面，果蠅有辨識記憶氣味的能力，以年輕果蠅的效果較佳；顏色訓練方面，果蠅亦可分辨記憶顏色；密集學習方面，適當學習次數內，有助於增加果蠅的記憶能力，但過度的學習刺激會降低學習效果。並且，我們選顏色訓練中記憶較佳的一組進行迷宮實驗，經三次的岔路選擇，選出對顏色記憶最佳的果蠅，希望能探討訓練過的果蠅子代能否有較優良的記憶。至於記憶時間方面，一次氣味學習，果蠅在四分鐘內皆有記憶，且年輕果蠅記憶效果較強，達六分鐘；另外，多次氣味學習，果蠅於第四次訓練效果最佳，且記憶能力可達十二分鐘。希望藉本實驗報告，以期更瞭解果蠅學習與記憶的資料。

RNA 病毒在複製過程中容易產生錯誤，導致其族群具中有很大的遺傳歧異度，累積的錯誤再加上選汰的壓力造成往後之變異。由於RNA 基因體之病毒變異較大，使得RNA 病毒在單一寄主上具有quasispecies 的特性，提供病毒產生新基因體的機會以適應環境或演化成新病毒。例如流行性感冒病毒與之前造成恐慌的嚴重急性呼吸道症候群病毒(severe acute respiratorysyndrome,SARS)以及禽流感病毒 (avain influenza virus) 皆為RNA 病毒，意味著RNA 病毒知不穩定性，並容易造成一些目前我們無法及時反應的危害。大部分的植物病毒又為RNA 病毒，本研究將以竹嵌紋病毒 ( Bamboo mosaic virus , BaMV )及其衛星核酸 (satellite RNA, satBaMV)為材料，進一步探討核?酸序列之變異對其族群在複製競爭上的影響。