凸n 邊形等分面積線數量之分布探索
(一) 本研究首先導出ΔABC等分面積線移動所包絡出的曲線方程式,其圖形是由等分面積線段PQ(其中P、Q皆在ΔABC的周界上)的中點所構成,具有3 條曲線段(分別為3 條雙曲線之一部分)的封閉曲線,形成內文所謂的「包絡區」。利用包絡區的區隔,我們找出:1.當P 點在包絡區內,則有3 條等分面積線。2.當P 點在包絡區周界上,則有2 條等分面積線。3.當P 點曲線段的端點或在包絡區外,則有1 條等分面積線。(二) 以三角形的研究當基礎,擴展到凸n 邊形(不包含點對稱圖形),我們發現:等分面積線數量之分布,仍然與包絡區息息相關,且1.凸2m +1邊形最多有2m +1條等分面積線。2.凸2m邊形,必發生內文所謂的「換軌」。因此,最多只有2m ?1條等分面積線。3.包絡曲線所分割出的區域,於相同區域其等分面積線數量相同,且相鄰兩區域數量差兩條。(三) 若凸n邊形有k個「換軌點」,則此n邊形過定點等分面積線至多有n ? k 條。(四) 若凸n 邊形為點對稱圖形(如正偶數邊形、平行四邊形),則所有等分面積線皆過中心點。1) Our study got a curve equation of bisectors of a triangle. When a bisector is moving, we get three curves. They’re constructed by the midpoints of PQ. The three parts of the three curves make a closed curve which we called “the Envelope Area”. We found out:\r 1. When Point P is in the Envelope Area, we can get 3 bisectors. 2. When Point P is on the curves of the Envelope Area, we can get 2 bisectors. 3. When Point P is outside of the Envelope Area, we can get only 1 bisector. 2) Based on our study of triangles, we found that in Convex polygons(not including Point Symmetry Convex polygons), the distribution of bisectors is related to the Envelope Area. 1. We can get at most 2m +1 bisectors in a 2m +1 Convex polygon. 2. We can get at most 2m ?1 bisectors in a 2m Convex polygon, and the bisectors on the curves will “Change the Track”. 3. Envelope curve will divide a Convex polygon into several areas. The same area has the same numbers of bisectors, and the near areas have less or more 2 bisectors. 3) If a Convex polygon has k points to change the track, it will have at most n – k bisectors.\r 4) In a Point Symmetry Convex polygon (ex. Regular 2m convex polygons and parallelograms), all the bisectors will come through the center point.
The garnets of the schlich of the winter coast (the White Sea)
During an expedition to the White Sea Winter Coast, samples of schlich with numerous garnets were collected. The coast itself is primarily a set of high steeps of sandstones and mudstones with no garnets. On the beach, however, there are numerous pebbles of metamorphic rocks, and many of them contain garnets. They were brought there by the Quaternary glacier and the present day glacier activity. Their source could be the existing or fully eroded metamorphic rocks of the Kola Penninsila and Northern Karelia.\r Goal of the research: To discover the possible origin of the garnets.\r Tasks: 1) To analyze the structure and the chemical composition of the garnets. 2) To study the works on the garnets of the Kola Penninsila and Northern Karelia in order to compare the information to the results of the analysis.\r Methods: 1) Granulometric analysis; 2) Magnetic and electromagnetic separation; 3) Microscope study of the garnets; 4) X-ray diffraction analysis; 5) X-ray fluorescence analysis. \r RESULTS\r 1. The sample garnets could be divided into two types: the bright red and the pale pink.\r 2. Both types are almandines with spessartine components. The pale-pink one contains Arizona ruby components, and the bright red contains andradite ones. \r 3. Only a few samples from Khangaz Varaki, Malye Keivy, and Tersky Coast are similar to the garnets that we collected. It is possible that the glacier brought them from the Kola Penninsula, but it is also possible that the rocks, where the glacier brought our garnets from, have been totally eroded.
橡膠鍵鏈結構與自由能的關係
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.
太陽短期活動對地球磁場與大氣溫度異常的影響
This study analyzed how short-term solar activities interact with the earth atmosphere, by using two statistic methods: Diffusion Entropy Analysis (DEA), and Standard Deviation Analysis (SDA). Since solar activities influence the Earth atmosphere in its radiating heat and magnetic field, we use DEA and SDA to calculate the exponents, H and δ, of the scaling law in three time series: “the intensity of solar flare” (representing by SOLAR H-alpha flare index), “magnetic anomaly of magnetosphere” and “sea surface temperature anomaly”. The values of H and δ show the time memory and correlative relationship between the event and next event happening in time series. When H = δ = 0.5, events occur in random. When 0.5
綠色陶土分子篩-污染大剋星
現今日常生活充斥著有機污染物,然而處理含有有機污染物的廢水需要極高的成本,有鑑於此,我們參考Fenton Reaction,從成本、毒性、活化能、操作方便性、二次污染及經濟效益的多方考量下,選擇以分子篩來固定鐵、鈷、鎳、錳、鋅之金屬離子,並決定以鐵分子篩為研究主軸,並探討其催化過氧化氫對有機物的分解。鑒於粉末狀的分子篩容易流失,我們以陶土固定分子篩,製作成反應杯槽,發現了分子篩與陶土的結合性。接著藉由二氧化碳感測器及光譜儀來感測有機物的分解速率,在控制溫度,濃度等條件下,探討分解有機物的反應及其反應時的特性。由實驗結果得知,分子篩能有效分解簡單醇類、氯仿、四氯化碳及indigo。使用0.35克陶土鐵分子篩,1M 以下的雙氧水50ml,其分解異丙醇所生成二氧化碳的速率可達0.34-0.55ppm/sec 之間(3.1-4.9×10-9mol/sec),此外有機氯化物分解後生成無毒性的氯離子;indigo染料分解後褪色。本實驗證實,陶土鐵分子篩:一、可以重複使用;二、可在較低濃度環境下運作;三、在酸性較弱環境下運作;四、可在低溫環境下運作(10℃);五、不須對大量鐵離子做沉澱回收的工作(此五點優於Fenton Reaction)。相較於TAML 等人工合成的催化劑雖有避免污染的優點,但卻有無法重複使用的缺點,綜合以上幾點看來,陶土鐵分子篩在操作方便性及經濟與環境保護上具有相當的潛力及價值。With organic pollutants everywhere and the high cost to dispose of them, this study, a two-stage experiment, aimed first to evaluate the efficiency of zeolite with different metal ions and then to compare their rates in reacting to the decomposition of organic matter with hydrogen peroxide as the catalyst. Since zeolite powder can be easily washed away, we tested zeolite with clay to hold such metal ions as Fe, Co, Ni, Mn, and Zn and finally used the Argillaceous Fe-zeolite for its superiority on the basis of cost, toxin, activation energy, easy operation, and contamination. A carbon dioxide sensor and a spectrometer for visible light were used to measure the decomposition rate of organic matter under controlled temperature and resolution concentrations. The results of the experiments showed that zeolite achieved excellent effects in decomposing organic chlorides such as lower alcohols, chloroform, and carbon tetrachloride. When 0.35g of zeolite and less than 1M of hydrogen peroxide resolution were used the rate of carbon dioxide production reached 0.34-0.35 ppm/sec (3.1-4.9x10-9 mol/sec). The decomposition of organic chloride produced nontoxic Cl and the indigo dye faded after it was decomposed. Our experiments proved that Argillaceous Fe-zeolite has the following five advantages over Fenton Reaction. First, it can be reused. Second, it performed well at lower concentrations. Third, it worked well under weak acid conditions. Fourth, it worked at a lower temperature (20℃). And finally, there was no need to recycle a large amount of Fe ions. Argillaceous Fe-zeolite was also found to be superior to TAML, which has the advantage of avoiding contamination but is not reusable. The above observation and discussion demonstrate that Argillaceous Fe-zeolite possesses very significant value in terms of easy application, economy, and environmental protection.
灰階影像內容之檢索技術
資訊時代的來臨,促使我們的社會型態大幅改變,無一不朝數位化的方向邁進。網際網路與資訊科技的快速發展,近年來影像資料庫和數位圖書館大量的成立,關於影像資料檢索的研究已漸漸成為一門極為重要的研究議題。在本研究報告中,我們提出一種植基於向量量化編碼法的灰階影像檢索技術。向量量化編碼法是一種極為簡單的影像壓縮技術。我們應用這個編碼法,來萃取出灰階影像內容的特徵值。同時我們也計算出整張影像與影像中間位置的像素平均值,作為日後檢索影像時過濾掉影像資料庫中不需要比對特徵值的依據。\r 我們所提出的方法能有效地萃取影像內容的特徵值並且讓使用者可以快速且正確地查詢到所需要的影像。當影像資料庫中存在與查詢影像完全相同的影像時,我們的檢索技術都能在第一時間第一順位檢索出這張影像。即便影像資料庫中不存在與查詢影像完全相同的影像時,我們的檢索技術平均74.3%也能在第一時間前五個順位檢索出最相似的影像。\r \r With the coming of the information age, our sociological system change extensively, and everything has moves toward digitization. Due to the rapid development of Internet, information technology, the rapid growth of image databases and digital libraries recently, the related researches of image retrieval have become a very important issue. In this memoir, we propose an image retrieval scheme based on the vector quantization to retrieve similar images from the image database according to the pre-collected image features. Vector quantization is a very simple image compression scheme. We have applied vector quantization to extract features from grayscale image. In order to speed up the retrieval process, we also calculated the mean pixel values of whole images and the central part of the image to filter the images, which are significantly dissimilar to the query image.\r The experimental results show that our proposed approaches can effectively extract features from the image and enable users to retrieve images from image database quickly and accurately. When images stored in image database match query image, the proposed scheme can instantly retrieve the stored image at the first rank. Even though images stored in image database query image exactly, the proposed scheme can instantly retrieve the stored image over 74.3% at the first five ranks.