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Generalized Petersen graph P(n,k)，定義為n 為不小於2 的整數以及1≤ k ≤ n−1，有頂點{ u0, u1, . . . , un−1, v0 , v1 , . . . , vn−1 }，及路徑{ uiui+1 , uivi , vivi+k：1≤ i ≤ n−1 }。在 [2] 中，我們可以知道P(n,5) 是Hamiltonian 等價於當n≠11。 在這一篇報告中，我們證明當generalized Petersen graph P(n,5) 是hyper Hamiltonian（一種Hamiltonian graph 再去掉任何一點後，仍然是Hamiltonian graph）的充要條件是n 為不等於11 的奇數且n ≥ 7。 The generalized Petersen graph P(n,k), n ≥ 2 and 1≤ k ≤ n−1, has vertex-set { u0, u1, . . . , un−1, v0 , v1 , . . . , vn−1 } and edge-set { uiui+1 , uivi , vivi+k：1≤ i ≤ n−1 with subscripts reduced modulo n}. And we can know that P(n,5) is Hamiltonian if and only if n≠11 from [2].In this paper it is proved that generalized Petersen graph P(n,5) is Hyper Hamiltonian (A Hamiltonian graph can still be a Hamiltonian graph when any one of the nodes fault) if and only if n is odd and n≠11.

本研究主要分析氣象因子對於灰面鵟鷹春季過境八卦山區之影響。分析1994年至2004年灰面鵟鷹遷徙資料發現彰化八卦山區之微氣象與灰面鵟鷹族群遷徙波動性具有顯著的相關性，其中以日平均氣壓、日平均相對濕度、日平均風速及日平均風向等氣象因子分別對起鷹、落鷹之族群數影響最為明顯。而其遷徙週期之動態變化，明顯地集中於約16日內完成主要族群之遷移。不論是同一年度內之高峰期變化，或是高峰期與日期契合之相關性，顯示氣象因子為其遷徙影響的重要因子。然而，從各年度間的遷徙高峰期間的相關性分析結果得知，目前11年過境調查紀錄，應該無明顯的規律性動態變化模式，考量其他對於遷徙過程可能具有影響的因子，應有其他的環境或生物因素影響遷徙期間族群的波動性及週期性。對於建立其遷徙模式而言，可能需要更多且更詳盡的遷徙紀錄，以及配合遷徙過程的各過境點的氣象或其他因素合併分析，方能獲得更為明確的結果。The main purpose of this study is to find the effects of the meteorological factors on the dynamics of the migrating population observed at the Pakuashan area in spring for the gray faced buzzard. The migrating population dynamics observed at the Pakuashan area correlated significantly with the local meteorological factors noted from 1994 to 2004. The daily average atmospheric pressure, average relative humidity, average wind speed and wind direction had significant impact on the soaring and landing populations of the gray faced buzzard. Obviously the annual migrating dynamics observed at the study site was accomplished within 16 days. In addition, the similar variation pattern of the peak migrating populations in the same year as well as the consistency of the date of the peak population observed annually supports the hypothesis that the local meteorological factors have a great impact on the migrating behavior of the populations. However, the correlation analysis of the peak migrating populations among years indicated that little cyclic migrating pattern was found in the past 11 years’ observation records. Other biotic or abiotic factors might have influence on the periodicity and fluctuation of the migrating populations. In order to establish a precise population model to describe the migrating behavior of the gray faced buzzard, detailed records of the migration process and the analyses of the relationships among the meteorological data as well as other factors and the bird populations observed should be gathered and performed.

台灣大多數學校並無全面性脊椎側彎篩檢與追蹤的健康服務，因此學生脊椎側彎的問題都不易被發現。本研究的目的希望藉由長期的追蹤與鼓勵學生進行治療，以降低脊椎側彎的盛行率與側彎角度。台灣地區學齡兒童脊椎側彎的盛行率大約是3-3.5％，而本校脊椎側彎的盛行率大約在1％左右，而且女生明顯多於男生。根據篩檢發現本校脊椎側彎較易發生在BMI（Body Mass Index）值較低的學童身上，也就是說，瘦型體格罹患脊椎側彎的機會較高。脊椎側彎可以藉由簡單的目測及儀器測量實施篩檢，並配合醫師復健運動，可達預防與治療之效果。本校實施兩年即約有60%的成效。因此建議將脊椎側彎納入學校健康檢查的項目之一（包含國小五、六年級與國中階段）。 ;The scoliosis of school children cannot be discovered easily because the overall scoliosis screening and tracing are not provided in most schools in Taiwan. The main purpose of this study is to reduce the prevalence rate and the angle of scoliosis by proceeding scoliosis screening continuously, and encouraging the patients to take physical treatment at the same time. Compared with the scoliosis prevalence rate in Taiwan(3-3.5%), the rate in our school is about 1%. Furthermore, the girls with scoliosis are outnumber the boys with the disease. This study shows children with low BMI value will have higher probability to acquire scoliosis. In other words, thin children may fall victims of the disease more often. The scoliosis can be examined with some easy methods, such as unaided-eyes measuring or scoliosis detecting. Besides screening, hospital treatment can attain the effects of prevention and cure. For the first two years, the practice of scoliosis screening in our school can improve the disease obviously (about 60%). In conclusion, the study strongly suggests the scoliosis screening can be included into an item of health examination from the fifth graders to the ninth.

隨著工商業發展，環境污染日益嚴重，對多數生長在這塊土地上的人，無疑造成了非常嚴重的影響。但若想要監控目前環境中的空氣品質，則必須具備專業的訓練，及昂貴的實驗設備，對一般民眾而言，根本就做不到。\r 藉由指標植物對所生長環境的高度敏感性，可以發展出一套純天然且免費的環境污染偵測器，不但方便、免攜帶、無須高級儀器協助、更不需要專業的分析技術。為此，我們以對二氧化硫等空氣污染物極為敏感的地衣作為指標植物，對其進行生態與環境污染關係的一系列觀察，並設計相關的實驗，找出環境污染物對地衣的實際影響，使其能夠實際的應用於日常生活，並可加以推廣，讓人人都可以利用地衣來了解自己所處的環境是否遭受污染，為自己家園的環境優劣把關。\r \r 文摘要 :\r With the development of industry and business , environmental pollutions become more and more serious . Undoubtedly , those pollutions have a great effect on us.\r However , by the means of the indicator plant which is highly sensitive to its environment , we can develop a set of natural and free environmental pollution detectors . In this project , we use lichenes,which are very sensitive to air pollution , to do a series of observations and to find out the influence the pollutants have on lichenes . If we can apply this to our regular lives , everyone can use lichenes to see if their environment is polluted or not .

This study tries to reveal how the velocity of flow influents the orientations and scattering patterns of the two-valve shells (we use Pecten in this study) during depositing processes by comparing the laboratory studies with the field observations. We learn from the laboratory experiments that the shells deposit at random directions when they are too crowded and are oriented to a certain direction when they are more scattered. We also find out that the shell fossils whose dorsal sides towards downstream with upward concaves are most likely to move. On the contrary, the shells whose dorsal sides towards upstream with downward concave are the most reluctant to move Examinations of the outcrop of the bedding of Pecten fossils, which are located near Long Dong, the northeastern tip of Taiwan, show that a lot of the shells settled along a certain direction and most of their concaves are upward. However, some of the shells with obvious orientation have downward concaves, which implies the depositional environments were under high current velocity. And the numbers of the shells whose dorsal sides are oriented to Northern East are about equal to those whose dorsal sides are oriented to Southern West. This result coincides with the results of the laboratory study. However, the experimental results can apply to the field analysis under certain assumptions.本研究就影響貝殼排列的水速作試驗，尋找水流和貝殼排列的關係，並和地層中實際的貝類化石做比較，藉以回推古老沉積環境。結果發現大量貝殼集中的情況下，貝殼間彼此的影響力會大於單純的水流沖擊；當貝殼較分散時，可以看出貝殼的頭部皆會一致朝向水流的來向作排列。而最適合移動的型態是凹口向上且頭部不朝水流來向的貝殼，而最穩定的型態是頭部朝水流來向的凹口向下貝殼。觀察實際地層，貝類化石大致上也有方向性的排列且正反面貝殼都有，可以推得當時沉積的水流大，故有足夠的動能讓貝殼重新排列。但由於試驗環境定和自然環境有所差異，仍有限制存在。

由於低廉成本、無毒及其他原因，由二氧化鈦、有機染料及電解液所製造的光敏有機太陽能電池(DSC)被預測即將成為一種大規模廣泛流行的太陽能電池。本實驗比較合成染料(像紅汞和疊氮離子)及成本較低且無毒的天然植物染料用於太陽能電池的效能。有些天然植物染料的效能大於合成染料的效能，像是紫色高麗菜、地瓜……等。在研製太陽能電池的過程中, 本研究利用自製的幾丁質燒結出的奈米顆粒成效極佳，不但粒徑大小符合，在燒結的過程中也不需經過物理研磨及介面活性劑的輔助，並且在低溫下即可燒結，並由BET 和SEM 測得幾丁質燒結的TiO2 的孔隙度大於標準燒結的TiO2 的孔隙度，因此本實驗決定利用去乙醯化之幾丁質扮演太陽能電池的二種角色:介面活性劑及保護劑。在本實驗中，部分的電池效能不盡理想，或許是因為所有的太陽電池樣本均使用相同的電解液(I3-)。要找到每種太陽能電池最適合的電解液則需要更多的研究。Because of the desirable features of low cost, non-toxin, and other reasons a dye-sensitized nanostructured solar cell (DSC) composed of nanocrystalline TiO2, organic dyes and electroiytes is expected to be in prevalent use. This study compared the differences in the functioning of different dyes in the solar cells, specifically those between the synthetic dyes, such as Merchrochronate and Polypyridyl complexes of ruthenium (N3-), and dyes made of natural plants which cost less and are not toxic. Some natural dyes, such as purple cabbage, sweet potato, etc, were found to have better efficiency than the synthetic dyes. The study makes use of self-made chitin to sinter nano particles, and the result is excellent. First, the particle radius meets the size requirements. Second, in the process of sintering nano particles, no physical pulverizing or surfactant assistance was needed. Third, the nano particles can be sintered at a low temperature. Fourth, from BET and SEM measurements, the degree of aperture of TiO2 sintered with chitin is superior to that sintered with Triton X-100. For these reasons, the de-acetylated chitin was chosen to serve as surfactant assistance and protector in the solar cells in this study. The study also found that some solar cells were not efficient enough. Maybe it is because all the samples of solar cells in this study were produced with the same electrolyte (I3-). Further study is needed to figure out the most suitable electrolytes for each solar cell.

洗潔劑分散系泡膜的變化十分有趣，是否能用吹泡法比較表面張力大小？沾黏在立體的框上會怎麼樣？能否由框上薄膜面積大小討論界面劑的化學性質呢？

奈米的科學與技術將是21 世紀所要探討的方向。在了解奈米粒子的表面效應、小尺寸效應、量子尺寸效應、宏觀量子隧道效應後，發現其應用甚廣，諸如再生物、醫學、環境、國防、工業產品等方面，都將佔有很重要的地位。我們主要是利用溶膠-凝膠法來製造二氧化鈦奈米粒子，並了解二氧化鈦奈米粒子可吸收紫外線及光催化反應，將廣泛應用電子、紡織、塑膠、橡膠，空氣淨化及廢水處理方面。本實驗將利用二氧化鈦的吸收紫外線特性，來研究其應用在化妝品上面。The science and technology of nanomater will be the direction we will explore in the 21st century. After understanding surface area effect of nanometer particle, Small size effect, Quantum effect, and Macroscopic quantum tunnel effect, we can diswver the application is very far-fluing. For example:biochemistry, medical science,eneironment,national defense and industrial products,will devine a very important position.We mainly use sol-gel method to produce U-TiO?,and understand the absorption of UV and photocatalysis,plastics,mbber,purging air,and dealing with effluents.This experiment will use characteristic of absorbing UV of U-TiO? for researching the application of cosmstics.

隨著科技的發達，工業廢棄物應運而生，在地小人稠的台灣，每年就產生約6000 公噸的廢觸媒，為了讓環境免於遭受廢棄物的污染，本實驗著重於廢觸媒的再利用，探討廢觸媒作為混凝土中礦物摻料對水泥(砂)漿流動性的影響。 本實驗所採用的廢觸媒來自石油裂解廠的靜電集塵廢觸媒，主要由SiO2 及Al2O3 所組成且具有部份非結晶相和卜作嵐材料之特性，外觀為乳灰白色粉末、含水量2.8﹪，溶於水中有放熱現象，pH 值為3.85。廢觸媒對水的親和力大，添加至水泥(砂)漿中會使得漿體的流動性減小，因此必須藉由提昇強塑劑劑量才能提高工作度。 在水膠比(W/B)為0.42 時，隨著強塑劑HPC-1000 劑量的增加，水泥漿的流度明顯增加，而且適當量的廢觸媒取代水泥，能維持水泥漿一定的流度。當強塑劑HPC-1000 劑量為3.0﹪、砂/水泥＝2.75 時，隨著水灰比(W/C)的增加，水泥漿的流度也明顯增加，而同條件下，不論水膠比(W/B)0.485 或0.55 時，廢觸媒取代水泥之水泥砂漿的流度比飛灰、爐石、高嶺土好，與矽灰相當，其最佳取代水泥量為15﹪。 As technology continues to develop, a considerable amount of industrial wastes have been produced.In Taiwan, over 6,000 tons of spent catalysts were brought out yearly. If such wastes can be reused in some ways, it may be helpful to protect our environment from being polluted. This study was taken to determine the influence of spent catalysts on the flowability of mortar while the catalysts were used as mineral additives for concrete. Since the catalysts could reduce the flowability of cement pastes because of the affinity between the catalysts and water, it was necessary to have superplasticizers added to improve the fluidity of the mortar. The spent catalysts used in this study were spent electrostatic precipitator cracking catalysts, called Epcat, which were provided by petroleum refining companies. Comprising mainly silicon oxide and aluminum oxide, the off-white catalyst powder present water content of 2.8%, pH value of 3.85 and exothermic reaction with water. In this study, it was found that while the ratio of water to binder (W/B) was 0.42, the flowability of the cement pastes increased with the increasing addition of superplasticizers. Besides, the flowability of cement pastes kept steady while a proper amount of Epcat was used to replace cement.When the ratio of sand to cement (W/C) was 2.75, with 3.0% superplasticizers HPC-1000 added,the flowability of the mortars markedly increased while the W/C increased, and the replacement with spent catalysts made the mortars show similar flowability as silica fume but better flowability than fly ash, slag and kaolinite, no matter the W/B value of the cement pastes was 0.485 or 0.55. In fact, the best Epcat replacement for cement was 15%.

我們的研究報告，是對校園中所種植的各種變葉木所做的一個研究，經過一連串的實驗證明後，我們確信花青素對變葉木的光合作用會有所影響。接著，我們測定出未氧化的植物色素與已氧化的植物色素吸光能力有很大的差異，我們假設花青素可以吸收某些特定波長的光以防止植物色素的氧化程度過強，實驗後證明我們的假設是正確的。另一方面，我們預期花青素具有保溫的機制，故設計了一個在低溫下花青素可保溫的實驗以證明之，結果和我們的假設相符合。我們預期花青素可利用保溫的特性降低植物因低溫所造成的傷害，減少農業上的損失。This study is about the Codiaeum variegatum which is grown on campus. After a series of experiments, it was proved that “anthocyanin” has a significant influence on the photosynthesis processing in Codiaeum variegatum. A great difference in the pigment of plant’s light-absorbing ability between the oxidized plants and the non-oxidized ones was also found in the experiments. Therefore, it was supposed that anthocyanin could absorb some special range of wavelength to avoid the pigment of plant to over-oxidize. The result of this experiment is in accordance with our supposition. In addition, we anticipated that anthocyanin has the ability to stay warm. By a designed experiment we successfully found that the result is exactly the same as our assumption. According to the findings of our study, we expect the characteristic -- ”staying warm” of anthocyanin could be applicable to decrease the harm to plants caused by the low temperature, and thereby to reduce the loss in agriculture.