Based on Ampere，s Law, the magnetic field intensity of the solenoids is B=μ0μr?n?I, where μ0 is the magnetic permeability of free space, μr is the relative magnetic permeability, n is the number of coils per unit length and I is the solenoidal current. The end magnetic field of the solenoid must multiply by one half. According to the above result, it can be greatly strengthened by the addition of a ferromagnetic core. First, we observe three different inserted materials of coils (wood, iron and magnetite), whose magnetic induction in different solenoidial current. By experiment, when the iron and magnetite materials were inserted into the coil, it would produce larger magnetic induction. The calculated relative magnetic permeabilities of wood, iron and magnetite materials are 0.57, 18.37 and 18.32, which are close to the reported paper (1). When the driving field is removed, the fraction of the saturation magnetization of the magnetite is retained, which is called hysteresis and is related to the existence of magnetic domains in the material. In the second part, we change the frequency of circuit switch, which induced different current. Compared with the result of the first part, it would fit the result, which is the induced magnetic field is proportion to the solenoidal current. 根據安培定律，螺線管的磁場為B=μ0μr?n?I。其中μ0為真空中的導磁率，μr為相對的導磁率，n為單位長度的線圈匝數，I則為通入螺旋管的電流。至於螺旋管的端點磁場須再乘上1/2。所以根據上述的結果，當螺旋管插入鐵磁性物質，會增強螺旋管的磁場。首先，觀察三種不同的芯物質；非鐵磁性材料，軟磁材料，硬磁材料（木棒，低碳鋼棒，磁鐵棒）在不同的外加磁場下的感應磁場，得到芯物質的磁化曲線，而計算出來的相對導磁率分別為0.57, 18.37 和18.32與參考文獻(1)接近。而當外加磁場移走時，硬磁性物質的磁性仍然存在，稱為殘磁現象。在第二部分，我們改變線路開關的頻率。發現不同的開關頻率，會得到不同的螺旋管電流，而造成不同的感應磁場。再度驗證了感應磁場大小是正比於螺旋管電流的大小。

目前市面上可以轉換顏色的物品大多可是經由物理變化所控制的，而以化學發光的產品，往往都只能有單一顏色，例如螢光棒，當它被製造出來時，就註定了本身就帶某種顏色，難道光的顏色無法經由某些特殊反應讓其在不同顏色間轉換嗎 ?

The physiochemical properties of fullerenes have aroused wide interest, such as its ability to accept and lose electrons and relatively high reactivity that permit various modes of structural modifications. However, obstacles to further research include its complete lack of solubility in water and low processability.\r This project investigated the morphology and microstructure of a fullerene-grafted polymer as a potential candidate for better and novel systems for drug delivery. In this research, hydrophilic functionalities were introduced to the C60 fullerene by chemical modifications, through the attachment of poly(acrylic acid) (PAA) chain. The objective was to investigate the dynamics and the self-assembly properties of this polymer in aqueous solutions, and the knowledge gained would enhance the development of such system for potential applications in drug delivery and nanotechnology.

我們的研究包括兩部份，第一部份是實地調查訪問。瞭解地震成因、傷害及現有防震方法，並調查坊間各種建築物類型，及常見私自改變建築物結構現象，做為研究的基礎。第二部份為建築物抗震實驗。研究發現：牆面挖空、頂樓加蓋、樓層挑高，建築物會在該處產生弱點，由此斷裂。柱子數量相同下，散開時支撐力較弱。不對稱建築物遇震時會不自然扭轉且易倒。隔震素材恰當，能有效提高耐震力。滑軌、彈珠隔震效果很好，但位移太大，為實際建築所不容許。建物下加裝阻尼材料，能吸收部份地震能量，降低地震對建築物的危害，並有效控制位移問題，是良好的隔震素材。樓頂加裝消能設施亦能減震，但設計極其不易。 The research includes two parts. In the first part the work is concentrated on on-site visiting and investigation such as understanding the cause of earthquake, the damage and the preventive method currently available, investigating the different types of building and the phenomenon of altering the structure of an existing building without permission by government authorities which is popularly seen in Taiwan. These are considered as the basis of the research. The second part is the experimental study of earthquake resistance of a building. The test results showed that weak-point can be caused at the place where the existing wall is moved or an extra building is attached to the roof or the structure of building has extended space between floors, and fracture always occurs at the weak-point. If the number of columns of a building is the same, then the scattering arranged location of columns is weaker than concentrating type of arrangement of columns. The building having unsymmetrical structure will twist in uneven fashion that causes the building apt to collapse in case of earthquake. Employing proper vibration-absorption material can effectively increase earthquake resistance. Sliding rails and balls can provide satisfiable vibration-isolation effect, but can also cause too much displacement of building structure. Install damping material beneath the building can absorb part of the energy of earthquake, and decrease the damage, and can solve the problem of displacement of building, therefore, damping material can be considered as an ideal vibration-isolation material. Install energy-attenuation equipment can also reduce vibration but the design of the equipment is extremely difficult.

看到環球城市數學競賽2003年春季賽國中組試題中，一題有關方格遊戲的問題： \r \r 在一塊9 × 9的正方形方格紙板中，最多可以挑選幾個小方格， \r 使得沿著這些小方格的二條對角線割開後，原正方形方格紙板 \r 不會分裂為二片或二片以上(即沒有小片紙板會從原正方形紙板 \r 中“掉下來”)？\r \r 原題目雖然只有一種圖形解，但我們發覺在其他方格紙板中，圖形解不一，在對幾個圖形分析和研究過後，發覺“似乎”有其特定作圖法，而且可挑選的小方格數也頗有發展的地方，令我們覺得相當有趣，而且此題目和之前看過方格類的問題不大一樣，因此，決定以此問題當作科展主題，加以延伸、研究，自我挑戰。

本文中我們探討一個有趣的數列。這個數列有一個非常特殊的性質：將數列相鄰兩項的前項當分子，後項當分母，所產生的分數數列，恰好會出現所有的正有理數。 這個特殊的性質表示，可以將正有理數按照這個方式作排序，這個排序將完全不同於常見的正有理數排序的方法。 (1). 在正有理數的排序的結構中，我們做出許多有關於此數列的定理。 (2). 用數學歸納法證明此分數數列涵蓋所有正有理數，且每一正有理數只出現過一次。 (3). 將數列分割後，利用試算表製成數列規則表，並整理出快速的方法將數列表達出來。 (4). 將an 數列排成“樹＂的模式，可更快速的把正有理數寫下來。 (5). 最後，設計出搜尋正有理數的演算法，解決在分數數列中第n個正有理數會是多少；以及正有理數會出現在數列中第幾項的問題。 Let’s discuss an interesting sequence. There is a very special quality in it. In this sequence, choose two numbers, which are close to each other, and suppose the first number as “member” while the second one as “denominator.” Then we can get a fraction sequence that includes all of the positive rational numbers! According to this special quality, we can arrange positive rational numbers by the following method. Then we can get a brand-new way of the arrangements. (1). We can find many theorems about this sequence according to this special arrangement of the positive rational numbers. (2). We can prove the rule that this fraction sequence includes all of the positive rational numbers by mathematical induction. Furthermore, every positive rational number appears only once. (3). After dividing this sequence into several parts, we can get a sequence rule list by using trial balance and find a faster method to express the sequence. (4). Arrange the an sequence by the tree model. By this way, we can get all of the positive rational numbers much faster. (5). Finally, we can develop the operation method to solve the questions that what position would one positive rational number be in the sequence and what is the first, second, third or nth positive rational number of the sequence.

In recent years, sandstorms have seriously attacked Taiwan day by day. Combining with the observations of Central Weather Bureau and the satellite images of NASA, the study has been collected the data of suspension grain in decades. And the study hopes the sandstorms’ information could be observed in early period. Still it hopes to find out the possible transmission paths in the atmosphere. Then we know how to cope with sandstorms in early time. Sandstorms attack Taiwan frequently in spring, the end of the autumn and the beginning of the winter. Compared with the charts of sandstorms and the satellite images, we could broadly aware that the moving paths of sandstorms are related to the currents and the characteristics of the atmosphere. When El Nino happens, the times of sandstorms attacking Taiwan decrease, and that increase when La Lina happens. According to the results of spectrum analysis, there might be high peaks of a year and six months short period varieties. And low peaks of 2.2 years and 7 months period, tell us that the short period aerosol varieties should be relative with season changes, the long period aerosol varieties may be relative with the El Nino and La Lina period. 近年來，大陸沙塵暴侵襲台灣的情況日趨嚴重影響。本研究中收集了近十年來懸浮顆粒資料，配合環保署空氣品質監測站、中央氣象局所觀測的資料與美國太空總署的衛星影像資料及NASA航空資源實驗室的氣流軌跡回推圖，希望能夠在早期觀測時發現大陸地區沙塵暴訊息，和沙塵暴所帶至大氣中的懸浮顆粒可能傳輸路徑。發生沙塵暴侵臺事件的季節，主要在春季及秋冬兩季交替期間發生的次數為最多。由地面天氣圖表、氣流軌跡回推圖及美國太空總署的衛星影像進行綜合比對之後，可大致瞭解大陸沙塵可能的移動路徑與大氣環流特徵有關。 聖嬰現象（El Nino）發生時，侵襲臺灣的沙塵暴次數會減少。在「反聖嬰現象」（La Lina）發生時，侵襲臺灣的次數相對增加。經由頻譜分析中得知，懸浮顆粒高峰期的變化有1年期及6個月變化趨勢，懸浮顆粒低峰期的週期變化有2.2年與7個月的變化趨勢，顯示短週期大氣懸浮顆粒變化應與季節變化有關，長期性變化或許與聖嬰反聖嬰週期有關連。

許多難纏的疾病，如神經退化性疾病與糖尿病，在1998年建立人類的胚胎幹細胞後，開始露出一線曙光。但就算科學家已經從胚胎幹細胞，成功引導出特殊種類與功能的細胞，預備做細胞治療時，需透過細胞核移植技術，使排斥的情形大大減少。所以當今年3月，韓國透過細胞核移植技術成功作出人類的胚胎幹細胞株時，轟動全世界。但是，他們從242顆卵，只做出一個胚胎幹細胞株，浪費這麼多卵子就牽涉到醫療倫理的層面了。既然，每一個人都要訂製自己的幹細胞株，那麼卵子的來源就很重要了。理論上，胚胎幹細胞可以分化成所有細胞與組織，當然也應該含生殖細胞在內。去年5月底，賓州大學就利用小鼠胚胎幹細胞，體外培養出型態上非常像卵子的細胞。所以，今年暑假利用兩個月時間，有個機會參與了台大醫學院婦產科的胚胎幹細胞研究團隊，稍稍瞭解了胚胎幹細胞製造成生殖細胞的過程。我們採取一種方法，先從胚胎幹細胞株，用類胚胎體(EB)的立體環境，加上 SSEA-1的篩選，與維他命A的刺激，引導至初始生殖細胞，第二步利用細胞重組的方法，利用小鼠胚胎的性腺組織，來支持這些選擇過的細胞，希望可以培養出小鼠的卵子或精子。我們從EB得到SSEA-1細胞約為全體細胞的10%，然後經過維他命A的刺激，得到SSEA-1細胞約為全體細胞的5%，這時的細胞理論上是初始生殖細胞 (PGC)，但是之後的體外單獨培養或與胚胎性腺重組培養，發現成果並不是很理想。到最後，也許受限於時間還有能力，沒有得到明確的小鼠生殖細胞，但是過程中，我學習到生殖細胞的生理，胚胎幹細胞的特性，基本實驗室的細胞培養與組織染色，這些都令我印象深刻。我們認為，如果有一個適當的基因轉植的胚胎幹細胞株，例如GFP放進生殖細胞相關的基因裡頭，讓達到終點，或邁向目標的細胞群，可以自我顯現，實驗會更容易達成目標。Scientists discovered ways to obtain or derive stem cells from early mouse embryos more than 20 years ago. Many years of detailed study of the biology of mouse stem cells led to the discovery of human embryonic stem cells in 1998. Through years of experimentation scientists have established some basic protocols or "recipes" for the directed differentiation of embryonic stem cells into some specific cell types. One major problem that must be solved before human stem cell therapy becomes a reality is the threat of rejection of the transplanted cells by the host's immune system. One way to avoid the problem of rejection is to use stem cells that are genetically identical to the host. This could be achieved by the same techniques of somatic cell nuclear transplantation (SCNT) that produced Dolly. Low efficiency less than 0.5% (1/242) in Korea this March brought some controversies in ethical issues. Where and how to procure the large amount of oocytes that will be required? One source of eggs could come from the generation of oocytes from embryonic stem cells (ESCs), as described by Hubner et al. (2003) in the mouse. By the selection of primordial germ cells (PGCs) and re-aggregation with their stromal cells, we hope to derive mature germ cells such as oocytes and sperm from ESCs in this study. In this study, we have demonstrated some PGCs after sequential selection by SSEA-1 antigen and optimal culture conditions. We also proved some FE-J1 positive cells but no further fertilization was obtained after all. Further investigation about this mechanism may be needed to derive these germ cells from ESCs.

本研究目的是探討大豆卵磷脂對於老化及學習記憶能力是否有改善之功能。以 24 隻 SAMP8 小白鼠，分為大豆卵磷脂組及對照組，飼養 8週。經由主動迴避試驗、單次被動迴避試驗，測其學習記憶能力；另測量其腦部丙二醛(MDA)之含量，評估其老化的程度。由實驗結果顯示，在主動迴避試驗中，大豆卵磷脂組被電擊次數有減少趨勢；在單次被動迴避試驗中，大豆卵磷脂組停留在明室的時間高於對照組。而在 MDA方面，大豆卵磷脂組腦中MDA含量低於對照組。由上結果推測大豆卵磷脂對於抗老化及學習記憶方面都有改善的功能。 The purpose of this research was to study the effects of soybean lecithin on improving the aging process and learning and memory abilities. The first part of the experiment is to raise 24 SAMP8 mice eight weeks, and divided them into group A and Group B. We tested them memory power by Active shuttle avoidance test and Single-trail passive avoidance test, and tested their degrees of the aging by the content of MDA. The result demonstrated that there was a decreasing tendency in times of being hitting in group A during Active shuttle avoidance test. The time which group A stayed in the bright room was higher than group B during Single-trail passive avoidance test, and the content of MDA in group A was apparently all less than group B in the experiment of MDA. So we can get the message that Soybean Lecithin has the improvement of ameliorating the speed of oxygenation and increasing memory power.

Root growth is related to the acquisition, distribution, and consumption of water and nutrients of plants. As a vital organ, roots directly take the effect of environmental change and its behavior is closely related to the growth of the whole plant. With such, the importance of root systems has motivated botanists to seek a better understanding of root branching complexity. This complexity, which has been difficult to comprehend using simple Euclidean methods (i.e. lines and circles), is important to the survival of plants, especially when the distribution of resources in the environment is scarce. Mathematical models using fractals and computers can be applied to accurately understand the growth and form complexity of plant root systems. This study was conducted to analyze the root growth of gamma-irradiated cashew and mangosteen using fractals.