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.
熱線式渦流流量計
流量計在實驗室與工業領域裡是重要的儀器，如今已經有數十種依不同物理原理而發展出來的型式，可以配合多變的環境需求與測量條件而使用。然而，各種流量計所適用的範圍備受侷限。本研究主要目的在發展一種熱線式的渦流流量計，供給氣體之流量量測之用。透過自行製作儀器與設備：熱線測速儀(包括探針、探棒及電子處理器)和渦旋產生器(管道中含一三角形截面之鈍體，當流體通過時，在後方尾流產生週期性渦旋逸放)。由於熱線測速儀擁有偵測流體運動時高頻動態變化的能力(約為20000 Hz 以內)，因此結合熱線測速儀與渦旋產生器，經適當的設計與調校，可以測得在不同流體流速時渦旋產生器的三角截面鈍體後方渦旋逸放的頻率。由於渦旋產生器的截面面積為固定值，因此可以從而計算出流量與渦旋逸放頻率的關係。經由嚴格的校準與驗證步驟，本研究的結果顯示自製的熱線測速儀擁有極佳的渦旋頻率偵測能力，所量測到的校準曲線顯示渦旋產生器的三角形截面柱所產生的渦旋逸放頻率與流量成線性關係。為了降低誤差，建議在0 ~ 40 CMM 之量測範圍內分成三條方程式來代表不同範圍內的校準曲線，最大誤差僅在5%以下。若需使用在不同的流量範圍時，僅需改變渦流產生器和幾何尺寸，以使渦旋逸放頻率適合於熱線測速儀的動態響應範圍即可。倘若商品化之後，可以實際應用於風扇流量量測、引擎進氣埠流量的測量等等應用。熱線測速儀本身也可作為風速計，適用於各種場合之風速量測。Flow meter is a instrument that is vital to the laboratory as well as the industrial related field. Based on different physical principles, tens of models that work in harmony with the diverse environmental demands and measurement conditions are developed to date. However, the application of varied flow meters is still under severe restriction. The purpose of this study is to develop a hot-wire type of vortex shedding flow meter for the use of flow rate measurement. Through the home-made apparatus and device, the hot-wire anemometer (includes probe, stem and electronic processor) and the vortex generator. (duct that contains triangle’s section of the bluff body. When fluid passes through, the wake behind produces periodical vortex shedding.) The ability of hot-wire anemometer when it detects the fluid moving changes of high-frequent movement is within 2000Hz, after appropriate design and adjustment, the combination of hot-wire anemometer and vortex generator may investigate the frequency of different flow rate that generated from the vortex shedding behind the bluff body of triangle section. The section area of vortex generator is constant value, thus it can calculate the relationship of flow rate and the frequency of vortex shedding. By means of strict calibration and test procedure, the results reveal that home-made hot-wire anemometer has excellent ability to detect the frequency of vortex shedding. The calibration curve indicates a linear relationship between the frequency of vortex shedding and flow rate. In order to reduce inaccuracy, it is suggested to classify three formulas to represent the flow rate that ranges from 0 ~ 40 CMM. The greatest inaccuracy is under 5%. When applied to different flow rate range, it only has to change the size of vortex generator only if the response frequency of hot-wire anemometer suit for the range of frequency of vortex generator. After commercialization, it can be applied to measure the flow rate of fans, flow rate of intake valve of engine, etc. Hot-wire anemometer also served as anemometer, which can be applied to wind velocity measurement in any situation.
台灣兒科病人罹患神經母細胞瘤者可檢測到微小病毒B19的存在
罹患神經母細胞瘤的兒科病人，尤其是罹患stage IVs 神經母細胞瘤者，他們有些伴隨著非常嚴重的貧血，但卻檢測不出神經母細胞瘤已經侵犯骨髓；有時病情來勢洶洶，尤其是腫瘤細胞中已可偵測到N-myc 基因增幅者，診斷時腫瘤細胞可能已在腹腔四處擴散並已侵犯大部分的肝臟。但是，某些這種病患，特別是腫瘤細胞中N-myc 基因沒增幅者，即使在沒有治療的狀況下卻可能有自然恢復的現象，也就是腫瘤細胞會自動消退，但原因仍待進一步的證實與探討。可是，這些病人在其病情最嚴重的時候，骨髓內紅血球母細胞形態上的改變顯示可能與病毒感染有關。但是關於病毒來源的研究，現有的資訊仍然十分有限，其中最重要的是，病毒感染與引發其後天之免疫作用是否有關，更需要深層的研究。因此，為更進一步了解罹患神經母細胞瘤之兒科病人的病毒感染及病毒蛋白表現的作用，我們這次研究的目的在檢驗罹患神經母細胞瘤及貧血之兒科病人與微小病毒B19 (PVB19)、Epstein-Barr Virus (EBV)、腸病毒71 型(EV 71)和巨細胞病毒(CMV)的關係，以及病毒蛋白表現對這些病人的作用與臨床意義。In pediatric patients with neuroblastoma, in particular, those with stage IVs neuroblastoma, sometimes the disease was combined with severe anemia. However, no tumor involvement was detected in the bone marrow. Although some of these patients may have N-myc gene amplification, and the disease could have invaded many abdominal organs, especially liver, interestingly, the disease might regress spontaneously in some of these patients. The medical reason of the spontaneous regression, nonetheless, remains to be determined. It is worth noting that morphological changes of erythroid progenitor cells in the bone marrow have suggested virus infection in these pediatric patients. However, the available information of viral origin is limited. Furthermore, it is possible that the virus infection in these patients could be associated with the revocation of immune responses related to the spontaneous regression of the tumor. In this study we will investigate the relationship of parvovirus B19 (PVB19), Epstein-Barr virus (EBV), enterovirus 71 (EV71) and cytomegalovirus (CMV) with neuroblastoma by PCR in Taiwanese pediatric patients. Moreover, we will study the effect and the clinical significance of viral gene expression as well as N-myc gene amplification in these patients.
費氏蛇
At the website “MathLinks EveryOne,” we found a problem “Snakes on a chessboard,” which was raised by Prof. Richard Stanley. The following is the problem. A snake on the m n chessboard is a nonempty subset S of the squares of the board with the following property: Start at one of the squares and continue walking one step up or to the right, stopping at any time. The squares visited are the squares of the snake. Prove that the total number of ways to cover an m × n chessboard with disjoint snakes is a product of Fibonacci numbers. We call the total number of ways to cover a chessboard with disjoint snakes “the snake-covering number.” This problem hasn’t been solved since it was posted on September 18, 2004, so it aroused our interest to study it. First, we used the way in which we added each block to the chessboard, and therefore we discovered some regulations about the snake-covering number of the1 × n , 2 × n and 3 × n chessboard. Through “recursive relation” and “mathematical induction”, we proved the general term of the snake-covering number of the1 × n , 2 × n and 3 × n chessboard. In the following study, we found a key method in which we added a group of blocks to the chessboard. Finally, we proved the general term of the snake-covering number of the m × n chessboard. Also, we discovered the way to figure out the snake-covering number of the nonrectangular chessboard.在網站“ MathLinks EveryOne ”中，我們找到了一個有趣的問題“棋然上的蛇” ( Snakes on a chessboard ) ，這個問題是由教授 Richard Stanley 所提出。問題如下：在m x n棋盤形格子上，蛇由任意一格出發，但蛇的走法只能往右 → ，往上↑，或停住 ‧ 若此蛇已停住，將由另一條蛇來走，且不同蛇走過的格子不可重疊”證明：將 m × n 棋盤形格子完全覆蓋的總方法數為費氐（ Fibonacci ）數列某些項的乘積。我們將把棋盤形格子完全覆蓋的所有方法數稱之為“蛇填充數” 由於這個問題自從 2004年 9 月 18 日被登在網站上後，還沒有人提出解答，於是引發了我們研究的興趣。首先，我們使用了將一個一個格子加到棋盤上的方法，並發現了 l × n 、 2 x n、 3 × n 棋盤形格子蛇填充數的一些規律。我們使用遞迴關係及數學歸納法來證明 l x n 、 2 x n ， 3 × n 棋盤形格子蛇填充數的一般項。在接下來的研究中我們發現一個特別的方法，一次增加數個方塊 ‧ 最後我們證明了，m x n, ，棋然形格子的蛇填充數的一般項 ‧ 而且，我們也找到如何求出不規則棋盤形格子的蛇填充數。
萬用虎鉗夾具
機械加工過程中往往遇到形狀複雜工件，無法用一般虎鉗夾持進行加工。若需加工複雜工件時，需使用V 形槽、壓枕……等等夾具加以輔助，但有些夾具根本無法夾持。若用特殊夾具需拆除原有之虎鉗，而且還必須校正，工作繁雜又浪費很多時間。 本設計之優點為不需更換虎鉗，直接放在虎鉗鉗口即可夾持不規則的物體，利用正向力的作用夾持而不打滑，輕易達到夾持時之穩定和足夠之夾持力，以達迅速、不需使用特殊夾具、不需再校正、可當平行塊之多功能夾具，使複雜形狀之工件加工簡單化、迅速化之設計。;When handling workpieces in complicated and irregular shape in the mechanical process, users are unable to make it with ordinary vises. V-block and clamping block might help, while some others do not work at all. In such cases, the user has to tear the vise apart and then do some correction, which is complicated and time-wasting. The strength of this design is that there is no need to replace the vise. The user just puts this device on the vise clamp to clamp the irregular object. The vertical clamping force makes the piece at work stable and allows no slipping. With this device, no special fixture or further correction is needed. It can also be used for a parallel block if necessary. In other words, as a fixture of multiple functions, the device makes the processing work simpler and more efficient than ever.