2008年

在實驗中學2007 年校內科展，參展作品《三角形中的切圓》的研究中，研究三角形內的切圓時，發現連續切圓的圓心與拋物線的軌跡有關。於是去查資料，在偶然的情況下，翻閱《平面幾何中的小花》時，接觸了「六圓定理」。因為覺得這問題非常有趣，於是便著手證明（見報告內文）。 又發現，當移動六個圓中的起始圓時，總是在某種情況下，六個圓會重合成三個圓。繼續研究其重合的狀況，發現了馬爾法蒂問題（Malfatti's Problem）的一種代數解法。 當我試著推廣六圓定理至多邊形時，發現奇數邊的多邊形似乎也有如六圓定理般圓循環的狀況，於是著手證明，但目前尚未證明成功。而偶數邊的多邊形則無類似的結果。 ;In 2007 National Experimental High School Science Exhibition, one of the exhibit works, "Inscribed Circles in Triangles", shows that the centers of the consecutive inscribed circles has something to do with the parabola's trajectory. To learn more about inscribed circles and parabolas, I referred to literature. By accident, I am faced with the problem on six circles theorem, in the book The Small Flower of Plane Geometry(平面幾何中的小花). Out of my interest in this problem, I tried to prove it. The other results are as follows: With the initial circle of six circles moved, in certain circumstances, the six circles merge into three. Further in studying this coincidence leads to an algebraic method to solve the Malfatti's Problem. Applying six circles theorem to the odd-number-sided polygons exists the same characteristic. It indicates that the inscribed circles will form a cycle. However, it hasn’t been successfully proven. The even-number-sided polygons show no similar results.

流體旋轉時，外圍及底部流體，因槽壁及槽底摩擦力的影響，流速較慢，相對的壓力也較大，導致外圍的水流會轉入中心。發現本實驗的渦流為強迫與自由漩渦組成。實驗中，探討f(轉動器的頻率)、H(總水深)、y(?入深度)、R(轉盤半徑)四者與角形數間的關係。若y、R 愈大、H 越小，隨著f 的增大，可觀察到的形狀邊數越多；反之，若y、R 愈小、H 越大，則f 愈高，所形成的圖形半徑愈大，易超過轉盤，不易觀察。依白努利方程式，外層水流的流速較慢，而內層水流的流速較快，故外層壓力大而內層壓力小，水會由外往內流，而此渦動流於轉動液面產生的剪力，可能為產生N 邊形漩渦的主要原因之一。流體旋轉系統中，因轉動而產生流體離心力與內外層壓力差交互作用下，於某特定相關的因素條件下，形成特定角形數漩渦，是本實驗的重要發現。When fluids are in rotation, fictitious force given by the container brings about the relative decrease of speed of the bottom and outer layer of water, which causes its pressure to increase, and water to spin inward, resulting in a vortex motion with N-corner polygons formed at the surface of the rotating plate. During this experiment, we discover that the vortices consisted of free and forced vortex and the polygons vary as control parameters f(rotation frequency), H(height of fluid), y(depth of the plate), and R(radius of the plate) change. The larger y and R are,the smaller H is, the more corners show up as f increases. On the contrary, the smaller y and R are,the larger H is, few polygons are identified since the rotating radius of polygons are larger than the plate. According to Bernoulli’s principle, smaller velocity of the outer-layer water causes water pressure to increase and water to spin inward. During this process, shear force is developed at the surface of the rotating fluid, which we believe is the main cause of N-corner polygons. In a rotating system, the interaction of centrifugal force and differential pressure causing a certain Ncorner polygon to be formed under different controlled parameters is our main discovery.

(a) Purpose of Research To investigate the wave conditions offshore along the South African coast to determine wave heights, intervals, and patterns. These results have demonstrated the power potential of ocean waves and identified sites for offshore power stations. The waves off of the South African coast are the most viable, as they have wave heights of between 2.7m (9ft) and 14.6m (48ft). It is also to assist in the development of my power station design, through research into offshore wave composition, principles, periods and characteristics. (b) Procedures I have used various calculations including the surface pressure of salt water per square meter to calculate the potential power produced by a buoy. These figures have been expressed in Kilowatt Hours, and are then able to be divided by the known consumption of a single USA household in 1 year. A figure of the amount of households that can be supplied by a single generator will then be reached. An approximate power output for a single buoy is between 200 and 300 homes per year (Dependant on wave height) A concept for a maintenance free electrical generator suitable for marine use has been investigated. The design will be made as: ● A working demonstration model capable of producing electricity, which consists of a Rotary Induction Generator, ● a scale model to show the appearance of one such generator & ● A large scale model to show how generators can be congregated to form a power station offshore. (c) Data Utilising the calculations of potential power output and the wave data, the financial viability of the generator has been calculated, in relation to current fossil fuel power stations, down to a cost per Kilowatt. Wave data from international marine monitoring websites that provide real time wave condition graphs, have been tracked by myself daily for over 1 month and recorded to provide a large data resource. This provides wave heights of multiple weather systems as well as averages. Costs have been investigated from Internet sources for electrical integration to the national power grid, as well as the generator manufacture. These are estimates, as the exact specifications of my device cannot be finalised without further prototypical research. (d) Conclusion With conclusions reached by thorough research into wave dynamics, weather patterns and their effects on wave heights, Rotary induction power generation and costs related to multiple power systems, I intend to demonstrate fully to the International Electrical Producers, that coal fired power plants are more costly and environmentally damaging than my revolutionary concept for a truly economically viable, ocean based generator system.

本研究探討運用磁場來達到非接觸煞車的功能，本實驗採用兩種方式來探討磁煞車力，分別為馬達有外加電流及沒有外加電流的情況。首先本實驗提供一穩定的電源使鋁盤轉動，觀察加上磁場及把電源切掉後鋁盤轉速的變化。實驗發現，當馬達沒有外加電流時，磁煞車力與轉速及磁場平方皆成正比；馬達有外加電流時，電流差會與轉速平方差成正比。探討磁煞車力與厚度及介質的關係，實驗結果發現，渦電流常數與厚度成正相關，且當兩片鋁片中夾有介質時，渦電流常數較小。 This experiment is based on the magnetic brake’s practical uses and braking forces. We want to calculate the braking force, and also examine the factors that cause the braking force to differ.We attached a metal disk to a motor to make the disk rotate, then we control the distance between the magnet and the metal disk, therefore measuring the relativity of the distance and the rotational speed. We discovered that when the metal disk received a large quantity of the magnetic field (close distance), the breaking force and the rotational speed increased. On the other hand, when the metal disk received a small amount of the magnetic field (far distance), the breaking force and the rotational speed decreased. The magnetic braking force will convert into kinetic energy, thus, by using this connection and also by increasing the electric current to measure the resistance, we calculated the magnitude of the magnetic braking force. Hence we perceived an inverse ratio between distance and the braking force, that is to say, the closer the distance, the stronger the magnetic braking force; the further the distance, the weaker the magnetic braking force.

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.

In the last two decades, there has been increased interest in the utility of quantum scale semiconductors. These fluorescent single crystals can be as small as 1 nm in diameter, and their size and shape has been shown to be controlled by the duration, temperature, and ligand molecules used in their synthesis. Quantum dots, provide clear benefits over the organic dyes currently used for tracking biological processes. Yet, as the production of quantum dots is often very costly, the search continues for finding an industry-ready synthesis for a quantum scale semiconductor which would have high yield, optimal durability, high luminescence, and a broad absorbance range. Silicon, in particular, has been of great interest as it is the second most abundant element on the Earth’s crust and is generally a bioinert and electrochemically stable element. We report the synthesis of water-soluble, luminescent silicon nanoparticles with potential applications to bioimaging. Through a solution state top-down approach, the synthesis of hydrogen capped silicon nanoparticles was achieved in various organic solvents. The surface of the nanoparticles was capped with the functional organic molecules rendering the Si-QDs both air and water stable. Cell studies performed with our silicon nanoparticles and human monocytes show the direct applications these particles could have for tracking biological processes and the progression of cancer in the human body. In attempt to shift the luminescence of these particles, alterations of experimental methodology was also explored in the areas of reaction solvent and heating time. Through these changes, shape control of silicon nanoparticles was achieved in the form of silicon nanorods. The synthesis of this new shape of silicon at the quantum scale was confirmed by ultraviolet spectroscopy, photoluminescence, and transmission electron microscopy. The results of this study indicate that the use of silicon nanocrystals for biomedical applications is feasible.

Smoothened (SMO) is a critical component of Hedgehog (HH) pathway that is essential for stem cell renewal and is dysregulated in many cancer types. SMO is a seven transmembrane domain protein with three intracellular loops. Primary structures of SMO intracellular loops are unique and very much conserved among the species, which is indicative of significant and unique roles in intermolecular or intramolecular interactions. The hypothesis was that synthetic analogs of SMO intracellular loops may function as HH pathway inhibitors. Derivatives of second intracellular loop were synthesized utilizing automated solid phase peptide synthesis based on Fmoc chemistry. Peptides were purified by HPLC and there anti-proliferative activity tested on melanoma cells by MTT assay. Targeted libraries of second loop derivatives of varying length helped to identify compounds that inhibited the growth of melanoma cells in vitro with IC50 in nanomolar range. The most potent of antagonists obtained is the palmitoyl derivative of the Nterminal half of the loop, and is 12 residues long. Lipidation proved to be critical for the activity. Remarkably, retro-inverso versions of the peptide, in which all amino acids are in D-configuration, are even more potent and have IC50 in subnanomolar range. Circular dichroism studies proved that the peptides are folded both in aqueous solutions and in the presence of lipids mimicking the membrane environment. They also suggested that retroinverso analogs have a different fold, which may contribute to higher activity. The new compounds are promising drug candidates and present convenient tools for solving the\r mechanisms of hedgehog signaling.

機械加工過程中往往遇到形狀複雜工件，無法用一般虎鉗夾持進行加工。若需加工複雜工件時，需使用V 形槽、壓枕……等等夾具加以輔助，但有些夾具根本無法夾持。若用特殊夾具需拆除原有之虎鉗，而且還必須校正，工作繁雜又浪費很多時間。 本設計之優點為不需更換虎鉗，直接放在虎鉗鉗口即可夾持不規則的物體，利用正向力的作用夾持而不打滑，輕易達到夾持時之穩定和足夠之夾持力，以達迅速、不需使用特殊夾具、不需再校正、可當平行塊之多功能夾具，使複雜形狀之工件加工簡單化、迅速化之設計。;When handling workpieces in complicated and irregular shape in the mechanical process, users are unable to make it with ordinary vises. V-block and clamping block might help, while some others do not work at all. In such cases, the user has to tear the vise apart and then do some correction, which is complicated and time-wasting. The strength of this design is that there is no need to replace the vise. The user just puts this device on the vise clamp to clamp the irregular object. The vertical clamping force makes the piece at work stable and allows no slipping. With this device, no special fixture or further correction is needed. It can also be used for a parallel block if necessary. In other words, as a fixture of multiple functions, the device makes the processing work simpler and more efficient than ever.

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。

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.