全國中小學科展

2011年

省錢大作戰-探討籬笆價格和所圍面積的關係

本研究探討在給定範圍的面積下,以最省錢的方式用籬笆圍出最大的矩形土地,其中矩形的邊長為正整數,且矩形對邊使用相同單價之材質的籬笆,但相鄰邊使用不同單價之材質的籬笆。我們希望透過轉換,將單價不同的情況回歸到單價相同的情況,以便完整的解決這個問題。\r 藉由改變邊長,將 轉換成 ,使問題轉換成相鄰邊之單價相同的情況;但是經過運算找出的最佳解 轉換回 後卻不一定符合「整數邊長」的要求(即 和 不一定是整數)。為了解決這點,我們重新以不同的角度探討單價相同的情形,以找出整數的最佳解。\r 最後我們發現,若 和 切線斜率的差值大於或等於1,則 坐標愈近 的解愈佳,而在差值小於1的範圍內,我們提出一個檢驗法,可以找到整個問題的最佳解,同時讓此最佳解 轉換回 後仍符合「整數邊長」的要求,進而解決問題。

Ring-shaped Round Wing

The purpose of our experiment is to analysis a specific ring shaped airplane called 'Round Wing' to know its characteristic. We've done several experiments to find its characteristics.\r First, Unlike other airplanes, Round Wing needs little time to recover its stability by comparing duration of flight.\r Second, as the eccentricity of the ring increase from 0.5 to 0.95, the stability and duration of flight are increased too. Also the size of body increase 1, 2, 3 times, the duration of flight is increased to 184%, 204%, 222%.\r Third, when Round Wings are attached each other by 2, 3, 4 they flew with high stability than before and stayed in the air much longer.\r Conclusion, Round Wing has unique characteristic (like high stability, and long duration of flight). And if additional power plant added, it can stay in the air very long. Also it can be used for leisure, patrol, broadcasting, and geological purposes.

以瑞利準則探討數位顯示之觀賞距離

本研究希望在數位顯示方面做些改進,利用電腦運算使戶外大型LED看板所使用之能源降到最低,以達到節能減碳。\r 本研究分為兩個部份:\r 第ㄧ部份:以瑞利準則探討亮點間距與觀賞距離之關係。\r 實驗中,以Photoshop繪圖模仿LED燈泡之排列,分析兩亮點之大小、距離與觀測距離的關係來設定點之尺寸,再進一步分析三原色點之觀測距離、比例及三原色點之佈點方式對混色效果之關係,並以瑞利準則判斷之。\r 得到公式如下:\r 自己所繪之點大小/點恰可分辨之最近距離=LED燈之間隔/點恰可分辨之最近距離=0.8mm/1m \r 第二部份:數位顯示—LED。\r 利用第一部份所得知的公式發現:在某ㄧ觀賞距離時,有最佳的影像品質且有最少的用電量。較近時,則影像品質降低;而較遠時,影像品質已無法提昇,而多餘的用電量則可經由實驗省去。藉由本次實驗結果,可利用所編寫之程式計算出在某ㄧ距離下最適合之燈泡尺寸及所省之電量,以達到節能減碳的效果。

燃料電池用之磺酸化SEBS-奈米粒子複合膜製備與性質研究

聚苯乙烯(S)-聚乙烯(E)-丁二烯-1(B)-聚苯乙烯(S) (polystyrene-block-poly(ethylene-ran-butylene)-block-polystyrene,簡稱SEBS)是目前直接甲醇燃料電池的質子交換膜研究中常用於與Nafion比較的膜材。Nafion的價格昂貴,且其高甲醇滲透率將造成電極毒化,故本研究探討不同製程與添加不同奈米粒子所製作之質子交換膜特性,以有效降低甲醇滲透。結果發現,添加之ZrP為層狀結構,增加甲醇通過親水區域端的難度,能有效阻擋甲醇滲透。且藉由磺酸根官能基團,以及本身帶有質子傳導性質,所以與Nafion的PTC數據差距不大,因此C/P值較Nafion高。未來可改變不同磺酸化程度,並在SSEBS內添加不同奈米粒子,並對於質子交換膜的持久性及實際應用之探討。

圓來如此─西姆松「圓」的研究

若從一個三角形的外接圓上取一點,作其對三角形三邊的垂足,我們知道這三點共線,是為西姆松線。\r 那麼當此點不在圓周上的情形呢?自平面上一點對一三角形的三邊分別做垂線,得到三垂足,並作此三垂足的外接圓,我定義其為:此點對此三角形的西姆松圓。這篇作品主要成果便是對西姆松圓的研究。透過不斷的研究,發現了許多關於西姆松圓的神奇性質,並得到了一些結果,主要的研究方向:討論共點、共圓、相似。\r 這篇報告是循序漸進的,後面的結果常用到前面的知識為基礎。此篇另一特點是:全篇的證明皆是自已給出的,採用方法皆為一般幾何證明,而沒有用到解析證明。\r 在研究過程中也得到關於著名的費爾巴哈定理及大上茂喬定理的另一種證明。

Fenorhythmes Of Yakut Taiga. The Calendar Of The Nature Of Olekminsk Reserve.

“Natural phenological per iodization of a year is called nature calendar…”\r The role of rivers in nature and man’s life is great. They connect people and cultures, form climate, give life to the thousands of living beings. \r In the tasks of researches there were:\r 1. To determine the peculiarities of seasonal dynamics of alive and inanimate nature of Olekminsk reserve;\r 2. To find out (to reveal) the peculiarities of phenological seasons of the territory of Olekminsk reserve. \r _ To determine of phenoindicators which are separate from phenological seasons \r _ To establish the middle dates of the advance of phenological phenomena \r _ To determine the duration of phenological seasons of a year.\r According to the general nature of plants the territory Olekma-Amga interriver refers to the provincial of pine-needles taiga zone, to Verkhne-Lensky flora area. Predominating part of the plants of the reserve relates to boreal types. The flora of the superior plants of Olekminsk reserve includes 654 types. The fauna of area is presented by 40 types of mammals from 45 living in the south of Yakutia, 187 types of birds, 2 types of amphibians and 2 types of reptiles.\r Besides, phenological researches were conducted on the testing area of school ecological control and during arranging of field ecological schools since 2000 till 2010. \r In all 169 phenological phenomena were analyzed from different phenological seasons of year for the last seven years. The gross amount of analyzed information composed 4000 information units.\r Results and conclusions:\r 1. The peculiarities of the seasonal changes of natural complexes were determined for the first time for south of Yakutia on the example of the territory of Olekminsk reserve. The calendar of the nature of Olekminsk reserve was composed. The analysis of phenological observations allowed establishing the row of phenoindicators, with the help of which we can determine advance of that or either phenological stage, as well as the disposition of current vegetative period can be forecasted. The information maybe used in organizing of the measures of nature protection, struggle with pests and the diseases of useful plants, parasite and tranmissive diseases of man and home cattle.\r 2. Geographic position and climatic peculiarities of territory form the peculiarity of seasonal rhythms of Olekminsk’ reserve’s nature.\r 3. All components of landscape in its seasonal changes tightly are connected with each other with causative-investigation ties having formed the definite complex of characteristic phenomena per the stage of seasonal development. \r 4. The carried out analysis of the primary materials of the Annals of the nature of the reserve and information from the field of ecological schools for seven years since 2001 till 2007 allowed detecting the peculiarities of phenoclimatic seasons of the territory of Olekminsk reserve.\r 5. Phenological and temperature outsets of phenological stages were determined.\r 6. Intervals and average of many years dates which are characteristic for phenological phenomena are determined.\r 7. The calendar of the nature of Olekminsk reserve was made on the basis of the processed information.

The role of miRNAs in plant development and virus defense

微型RNA是最近發現的小RNA,調控生物體內的反應,包括生長、細胞分化、對抗病毒…等。植物利用RNA干擾 (RNAi) 或過敏反應 (HR) 對抗病毒感染。有趣的是,miR168可藉由降解mRNA或抑制轉譯,調控阿拉伯芥AGO1的表達,而AGO1是RNAi的一個重要元件。miR398則調控銅鋅超氧化物歧化? (CSD1, CSD2) 的表達,而CSD1, CSD2負責產生過氧化氫去引發細胞凋亡 (cell apoptosis)。帶有竹嵌紋病毒 (BaMV) 全長基因的轉殖菸草 (Nicotiana benthamiana) 品系27-17是我們的研究材料。27-17的幼葉不具病徵,隨著葉子的生長,病徵會漸漸變嚴重。我發現被病毒感染時,植物會提高AGO1的表達,使RNAi更有效率。然而,病毒藉提高miR168使AGO1的量無法上升。植物亦可提高CSD1, 2 mRNA的量,促進細胞凋亡。病毒卻會引發miR398降解CSD2 mRNA。在病毒力價高的葉子中,雖然CSD2 mRNA降低且miR398升高,植物仍可大量提高CSD2蛋白的量。CSD1 mRNA沒有被miR398負調控,詳細原因仍有待研究。

The Main Features Of Climate Change On The South-West Of Yakutia In The Last 100 Years

1. Purpose of the research to detect the dynamics of the change of moisture regime on the territories of Olekminsk area for the past 100 years.\r 2. Procedures for analysis we used as materials of observations on the testing areas of school of ecological control of our Center, so and of the meteorological station Jikimda situated on the territories of Olekminsk reserve, as literary sources. Time-series analysis was conducted as to following scheme: for period 1901 -1914, 1949-1958 and for period 1996 -2009.\r 3. Data The changes of the temperature of air and sediments for the period of instrumental observations from 1901 to 2009 were analyzed\r 4. Conclusions Climate is characterized with many parameters coming in radiation, the heat and aqueous balances of territory. The most simple and widely measured parameters are the temperature of air and the quantity of atmospheric condensation. Carried out researches and the analysis of received results let us make tentative conclusions:\r 1. Average amount of precipitation increased on 41% (with 229 mm during the period 1901-1914 till 390 mm for period 1998 - 2006)\r 2. The decrease of firm precipitation in cold period and increasing of fluid precipitation in warm period are noticed for 100 years.\r 3. The gross amount of days with precipitation grows from 135 days (period 1901 - 1914) till 160 days (for period 1996 - 2006). For period 1901 -1914 a month with the greatest quantity of days with precipitation is January. The middle quantity of days with precipitation in it composes 16 days. A month with the least quantity of days with precipitation is July. The middle quantity of days with precipitation in it composes 8 days for period 1996 -2006. We should note that though increasing of the quantity of days with precipitation is on the cold period of year, increasing of the value of precipitation arises at expense of warm months. This reflects well the annual motion of the force of precipitation as to studied periods, the force of precipitation grows, in the first case achieving maximum in August, into second - in July. The maximal significances of the force of the precipitation of second period exceed of such the first period almost in two times.\r 4. The disposition of meteorological phenomena shows the change of climate to moistness. There are more days with fog, snow-storm, the quantity of days with precipitation increases from more 1mm, so more and 5 mm and it’s noticed that the quantity of days at a speed of wind more 10 and 15m/sec increases.\r 5. The change of the precipitation amount, especially in warm period affects the level and the expense of water in the Lena River. Analyzing as to decades the statistics on stratum of flow as to stratum flow since 1930 till 2006 can be noted tendency increasing of stratum flow from 132.8 mm in 1930 till 289 mm in 2006. The significance of the annualized expense of water with 6370 in 1999 till 8710 m/sec in 2006 enlarge, the annualized level of water changes from 282 till 376 cm. It is according. The area of the movement of the significances of the indicators changes to their increasing in the course of the year for the last 10 years. Averaging their significance exceed the norm of 18%.\r In conclusion we want to note that global change of climate actually touches all of us and already has significant influence on natural environment and the life of people. In simple words warming - the increase of temperature - for the many areas of our north country might become a favorable change of the conditions of life. But the trouble is that the change of climate is much more complex process, and one of its main manifestations is the augmentation of the instability of climatic conditions, changes of flora and fauna, increasing of infectious diseases. This influences badly on natural ecosystems and complicates the life of people. Besides, too quick warming does not let natural ecosystems adapt themselves, and they can be destroyed. And at least now we shouldn’t wait doing nothing, it is necessary to take all efforts to try to reduce climate change effect.

棋盤分割

本研究所探討的主題是一道分割棋盤的題目:\r 給定一個黑白相間的mxn棋盤(設m為縱向邊,n為橫向邊),將其分割成若干個面積大小都不等的矩形區域,且每個矩形的黑格和白格個數相等。設f(m,n)為符合上述條件的最多分割矩形的個數,則f(m,n)是多少?\r 在研究過程中,我們首先藉由對各棋盤進行分類,利用不等式的運算找出其中的關係,求得當m=n以及mn=k(k+1) 時(其中K為正整數)的f(m,n)值,並構造出其分割方法。而k(k+1)

植物miRNA的特殊長度─生成與演化

基因靜默為各種生物普遍擁有的調控機制,是以microRNA (miRNA)和Dicer-Like (DCL)與Argonaute (AGO)等數個蛋白質來完成。在植物,miRNA大多是由DCL1截切前驅物所產生,因DCL1具有21-nt 分子尺,所以絕大多數miRNA的長度為21nt。然而,其他特殊長度卻也有一定比例的存在,且可能有特殊的功能。最新研究發現22nt的miRNA可誘發更多的小片段干擾核酸來造成大量而強烈的基因靜默;然而,一般21nt的 miRNA卻無此功能。本研究以生物資訊的方法分析大量資料庫,並以分子生物學實驗佐證,探討特殊長度miRNA的生成、功能與演化。結果發現,20nt的miRNA可藉由對稱性與非對稱性縮短產生,這是RNA結構研究的新發現。功能上,20nt的miRNA與生長發育有關,22nt的miRNA則多與逆境反應有關;在演化上,長度20nt的miRNA呈現高保守性,而大部分22nt的miRNA則呈現高度物種專一性,為演化快速的特殊長度。