Miracles in life originate from daily life itself. What can be imagined can really be achieved. Hong Kong, as an international city, is small in area and densely populated. To utilize space, tall buildings inevitably emerge. Taking elevators has therefore become the daily routine of everyone of us. However, problems abound with the present elevator system. You have probably gone through the dreadful episode of waiting long for an elevator to come, and passage being interrupted by unreasonably frequent stops. Besides, it wastes space, since each elevator tube can only accommodate one elevator. This is why our Free-D Elevator System will revolutionize the present one. It consists of a large cylindrical tube, which can be divided into several smaller, imaginary sector-shaped tubes. In each small tube a large number of elevators move vertically by magnetic levitation. The elevators can also rotate from one tube to another, thereby avoiding collision. This innovative design will substantially increase the number of available elevators for given space. Most importantly, it is highly feasible.

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.

在理化課程提到「空氣中的氧約占空氣的1∕5」，但老師所提及的各項實驗，我們一一重做一遍，過程中發覺存在不少問題；例如採用悶熄蠟燭的實驗方法，似乎無法驗證這樣的結果；即使改以鋼絲絨生鏽方式驗証，至少也得花費將近一天的時間；因此我們想出新的反應裝置，以鋼絲絨通電使其燃燒的方式，發現可縮短實驗時間並達到準確驗證的目標。

電動車是解決空氣污染的重要工具，而高電能容量的電池則是其動力的來源，除了電池的蓄電量，電池的充電速度同時決定了二次電池在電動車上使用的價值，有鑑於一般傳統定壓充電餘充電後期的低壓差導致充電速度減慢且大量拉長充電時間的缺點，本研究以高電能容量的鉛酸電池微研究對象，研究各溶液濃度、溫度、極板條件下的最佳充電電流，並且將各極板、溫度、溶液濃度下的最佳充電電流以變壓差充電充電的程序應用於電池的充電，結果顯示；使用變壓充電程序之鉛酸電池確實可較定壓充電之鉛酸電池節省一半的時間。

二階遞迴數列與一般遞迴數列最大的不同之處在於一般遞迴數列的足碼是n的函數；而二階遞迴數列卻是n與An的函數，這代表在求出第n項不只需要參照前兩項的值，還必須參照過去未知項的值，而這個特殊的性質會造成有些二階遞迴數列因為無法參照而無法成立於是，我刻意不找出足碼的值是多少，而重點在於前後兩項足碼的〝差異〞，而因為在數列中有特殊涵義，因此特稱〝子元素〞。〝出現次數〞也是很重要的研究工具，因為每一項都必須參照過去〝未知〞項的值，這就代表了代表前面的值會影響後面的值。研究過程如下： 1. 找出子元素的性質 2. 利用子元素的性質找出出現次數的規律以及每個區間的影響範圍 3. 利用出現次數的規律找出一般項

科展的指導老師在高中發揮了極為重要的角色，他指導學生閱讀前幾屆的重要作品，提出是當的新問題，領導研究與討論，給予類似專家的常識性建議，有些甚至成為學生的共同研究者，我們看到優秀的高中科展作品中，有許多作品背後都有一個優秀的數學老師，以本屆為例如第一名第，第二名。 指導老師在小學更是作品之母。但是小學指導老師的定位，至今仍然非常模糊。在高中由於作品水準很高，教師不易越殂代庖，但是在國小，國中指導老師很容易不由自主的陷入教的陷阱，以至於許多人認為國小指導老師就是把材料成功地教給學生。其實這是極為錯誤的看法。例如初小組肥皂泡膜角度與經濟網絡的作品，我們注意四一Ｏ四到如果教師讓學生先實測各種泡膜的角度，在得出角度都是120度的經驗歸納結果。相信兒童對於自人界的現象的數學性會有更大的驚奇，如今教師先告訴學生120度的事實，再去檢查，這種「驚奇」的驚人浪費，令我們感到非常可惜。事實上，現在已經有少數小學老師已經覺察到，如果指導老師可以更早成立研究群，更有耐心，更願意傾聽兒童在做什麼，只要找出適當的問題，兒童一樣可以有探索研究的活動。只是這種活動還需要數學教育的學者做更進一步的研究已歸納其研究活動的特質，可?科展評審的參考。當然初小和高小的差異很大。至於適當的問題雖然難找，但也不是沒有。例如初小四一Ｏ一從數字方塊到數字八卦以及高小正多邊形分割成三角形的分割總數及類型都指出值得效法的新趨勢。 國中生正處於進入文字符號運作的尷尬期，加上國中各種測試卷的反覆練習繁多，剝奪兒童從事研究的時間，一向是科展最弱的一環。這也是本組第二名從缺的原因，其實國中組無強將，反而是指導老師可以大加發揮的地方。事實上，國中生透過科展活動也可以順利甄試昇學，由於名額較少限制，更應多鼓勵學生參與。 本屆和上屆來台的美國ISFF學生作品，都和代數數論有密切關係，事實上，高中生的極限觀念的發展，比代數抽象思考的方展慢。基於此點，建議高中指導老師可以給予學生初等數論以及初等待數數論的標準教科書研讀，增強其運作的層次，代數數論的應用很多，而且也很好，如本屆的問題是說如果「n」事一個個邊皆為有禮數的直角三角形的面積則有此解可以生出無線多個有理直角三角型面積都是n。 科展研究問題的開發一向是科展師生最頭痛的問題。有一本英國空中大學教授MASON所著的「大家來數學地想」可以大大的拓展研究的想像力，數學傳播季刊，Mathematical magazine,Mathematical monthly,Mathematical Gazette,Fibonacci Quarterly,國際或亞代奧林匹克試題,Putnam試題都是傳統方法已外找材料的地方國小可從國中高中取材,但切忌獎什麼微積分代數等名堂。 另外科展老師也必須善於累績資源，以及累積自己的經驗與聲望，以吸引校內的優秀學生參與科展，本屆初小組四一Ｏ依從數字方塊到數字八卦和高中組四四一四方塊數論就是源自同一問題，但兩者的方展缺是大異其趣。四一Ｏ一大做奇偶類型經運作後演化的樹型圖，但四四一四在初步地用符號說明演化後，既一舉跳過此一過程，進入決定性的証明。其中的對比有如GORDON等數學家在不變式的工作和Hilbert一舉用一個存在性定理暫時地結束此一時期的歷史事件。另外科展老師也必須善於累積資源，以及累積自己的經驗與聲望，以吸引校內的優秀學生參與科展。

湖口台地為古淡水河等數條向北方海岸開展之順向河流以石門為頂點所形成的「古石門沖積扇」之一部份。此沖積扇面包括桃園台地、中壢台地、平鎮台地、伯公崗台地、湖口台地等，而以湖口台地為及南，其概略範圍東綠以 20 ~80 公尺高台地崖與大崙面（ LT3）相接， 70 公尺左右台地岩與中壢面（ LT 3 ）相接，西緣以 80 公尺的斷崖接坑子口附近海岸，北緣以約 6O 一 80 公尺的斷層崖接楊梅地溝帶，地溝帶之北即伯公崗與平鎮台地。南緣為關西、新埔間的鳳山溪河床，鳳山溪之南即為飛鳳山丘陵。台地東西延長 14.5 公里，東高而西低，東寬而西窄，形狀恰似一隻大火腿，而積達175.25平方公里。木台地在地形面上屬於紅壤（褚土）緩起伏面，簡稱 L . H 面 ( Lateritic highland）為中新世林口期時因地形、氣候的驟變突然堆積大量紅土與厚礫石層，地形面下可與平鎮、伯公崗相對比。古石門沖積扇各台地大致以扇頂（石門）為最高，而向西或西北海岸方向緩傾，湖口台地扇頂部份銅鑼圈附近卻有一中間較低陷部份，較南、北兩側各低 30 ~40 公尺定右，且這低陷部份由於較低，侵蝕力較弱，原面（300 公尺以上部份）保持十分良好，與其餘各地面有別，如此構成一個使湖口台地更復雜的地形景觀，造成一個值得深思的地形差異，這一低陷部份如何造成的？是否與南北兩側台地而同時形成？有否同屬一個面，都是值得探討的問題。

IF鋼在鹽酸溶液中之腐蝕速度隨鹽酸濃度之增加而增加。12M之硝酸溶液對IF鋼具最強腐蝕性，而最低(0.1M)及最高(16M)濃度之硝酸溶液對IF鋼之腐蝕性則相對較弱。硫酸對IF鋼之腐蝕速度則由低濃度至高濃度呈現極大變化，當硫酸濃度由0.1M漸增至3M時腐蝕速度亦隨之增加，爾後腐蝕速率減小，至硫酸濃度由8M時反而呈現極大之重量增加。由於表面腐蝕層不適於XRD分析，故由EDS結合FTIR分析得知H?SO?/8M-24hrs.情況下試片表面之腐蝕層為Fe?O?。由SEM觀察發現腐蝕速率較大之條件，如HCI/12M-1min.及HNO?/12M-1min.處理過後，試片表面甚至出現具晶體對稱性之蝕恐。由本研究之初步成果發現：是溫下可以利用中等濃度(如8M)之硫酸液來處理鋼鐵，使之表面生成一緻密之氧化鐵(Fe?O?)，達到防蝕之效果。IF (interstitials free) steel was processed in various aqueous acid solutions to observe the corrosion behavior. The corrosion rate of IF steel in HCI(aq) increases with the concentration of HCI(aq). HNO?(aq) with concentration of 12M was observed to be the most aggressive for IF steel. The corrosion rate of IF steel in H?SO? solution increases from 0.1M to 3M and then decreases gradually with the concentration. A large amount of weight gain even observed when the concentration was 8M. The protective layer produced during H?SO?/8M-24hurs. treatment was analyzed to be Fe?O? by using SEM (Scanning Electron Microscope), EDS (Energy Dispersive Spectroscopy) and FTIR (Fourier Transform infrared). Etch pits with crystallographic symmetry were observed on the specimens treated with conditions HCI/12M-imin. and HNO?/12M-1min. Processing condition H?SO?/8M-24hrs. could be employed in corrosion prevention for IF steel under ambient environment.

The Latin American and Caribbean regions have one of the biggest cultivable areas in the world, calculated at around 576 million hectares. Nevertheless, 16% of this land its affected by a kind of soil degradation. Previous studies have shown that the vesicular- arbuscular mycorrhizae (VAM) can fix phosphorus and other elements to plants, is an important micronutrients transporter, increases the water potential of plants, can bioremediate the lands affected and prevents lixivation. These effects are very convenient and can replace the chemical fertilizers which produce collateral damage to the environment. For the reasons mentioned above, this prototype for the production of vesiculararbuscular mycorrhizae, denominated as a biofertilizer, is presented. The prototype consists of an aeroponic system which disperses, in aerial form, nutrients to the host/trap plant roots where the fungus produces its mycelium web. The fungus propagation consists of an artificial union of isolated and identified spores of the mycobiont ,which we want to propagate, with the trap plant roots. The specimen identification consisted in a staining and clarification method (Phillips- Hayman), and a taxonomical identification. In order to prove the (VAM) benefits, two experiments using Sorghum spp. were carried out. One consisted of a comparison between the plants with VAM and a control without VAM. The second one consisted of a chemical comparison between control/fertilizer/ VAM plants. These two experiments were subjected to a water stress test for 10 days. The prototype achieved a production of roots mycorrhizae between 50-65% of colonization. The taxonomic identification corroborated that the mycobionts propagated and the controls were the same species. Experiment One demonstrated that the mycorrhizae treatment has more height, stem diameter, fresh/dry weight than the control which doesn't have VAM. We also conducted the Student’s t Test to check the previously mentioned hypothesis. In Experiment Two, the control and fertilizer treatments had a similar percentage of Nitrogen and Potassium, and the mycorrhizae treatment significantly increased these two elements; nevertheless, the fertilizer and mycorrhizae treatment obtained a similar percentage of Phosphorous. The water stress test was for 10 days - one month after planting. The results were: the fertilizer and mycorrhizae treatment had the same resistance to the stress, the mycorrhizae recovered faster from the stress and the control specimens presented a lower shrivel percentage than the other plants. One of the principal gains which this prototype has is that the trap plant doesn't die after collection, and the plant only needs to be inoculated once in the plant’s life because we only prune the roots. In nature 90% of plant species present some type of mycorrhizae association, hence the feasibility of this prototype for introduction, use and application of the fungus as a biofertilizer. 1 Centro de Bachillerato Tecnologico Industrial y de servicios N°24 2 Instituto Tecnologico de Ciudad Victoria

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.

近年來環境污染的問題日益嚴重，尤其在城市要汽車飛馳所排出的度氣和發出的噪音，逐漸威脅到人類的健康。為了改善這個問題，般近政府大力推展以馬達為動力的電動汽車。我們對於馬達這方面的知識感到好奇，同時也產生了許多問題，璧如(一)馬達為什麼會轉動？(二)影響要馬達轉動的原因有那幾種？(三)能不能設計一種簡易的馬達？於是我們把這些問題講教老師 · 老師指導我們做以下的實驗。