步步為營
Two soldiers walk on a checkerboard. They can only walk one step once a time and two directions, front and left, are decided randomly. The gunshot is the column and row where a soldier is located, and one will die if he enters the gunshot area of the other. To treat the probability of winning, we first study the cases of 1×n, 2×n, 3×n, and 4×n rectangles iterately. Then we establish a general form of the probability of winning in a general n×k rectangle by using recurrence technique and generating function, respectively. Finally, we extend to the general n×m×k cuboid case to obtain the first soldier’s probability of winning.在一個長方形的棋盤中，兩士兵行走，每一次只走一步，而且上和左兩個方向是隨機的，射程範圍是所在的此行和此列，而進入他人射程範圍則死亡。探討其獲勝機率，從1×n 、2×n、3×n、4×n 矩形的情形逐步研究，並分別運用遞迴式的技巧及生成函數，導出 n×k 矩形中先走士兵獲勝機率的一般式。更進一步地，我們也獲得了n×m×k 立體空間先走士兵的獲勝機率。
探討茶液成分受光及貯存時間之影響
Tea is the most widely accepted and consumed beverage worldwide due to its characteristic aroma and taste. Recent studies have provided the strong scientific basis for understanding the health promoting effects and cancer preventive actions of tea. The components of tea especial the catechins are varied with the conditions of making tea. To understand and determine the chemical composition of tea is very important. Some investigations of the parameters on the storage and making of tea were carried on in this study. The kinds of tea studied were including black tea, oolong tea, green tea, and instant tea bags. A high performance liquid chromatograph combined with UV detector and mass spectrometer used to analyze the components of tea. The results showed that the composition of tea solution is dependant of the exposure of light. One of the components of tea, (-)-epicatechin methylgallate (ECMG) was oxidized to quino form. The concentrations of (-)-catechin gallate (ECG) decreased and one of new compound (M.W. 442) produced with increasing the storage time. From the results show tea made with cold water is better than that made with hot water. The ingredients in green tea were changed faster than those in fermentative black tea and oolong tea. The components of tea can be kept unchanged for a long time at low temperature. In refrigerator, the time can be extended to overnight. 茶由於其具有特殊的芳香氣味及口味，廣泛地被世人用為飲料，近年來的研究證據顯示茶具有促進身體健康和防癌功效，但茶中成分之變化，尤其兒茶素隨茶的種類、茶沖泡保存方式及置放時間而有所不同，因此對於茶中成分及沖泡方式的認知是一門重要的課題。 本實驗主要是探討茶沖泡時間及貯存條件，對於茶液所含兒茶素變化的影響，探討的茶包含紅茶、烏龍茶、綠茶及其茶包。並使用質譜儀及高效能液相層析質譜儀配備紫外光偵測器分析茶液中之成分，實驗結果顯示成分變化速率以未發酵的綠茶較發酵的紅茶和烏龍茶快；低溫儲存時，亦可延緩茶液成分的變化，例如加蓋並存放於冰箱，則茶置放至隔夜其成分均未改變；同時結果顯示成分產生變化者，主要為兒茶素氧化，如將多酚類氫氧基經氧化變成?（quino） ，其次為斷裂再產生聚合其中綠茶以不照光變化較大。本研究並經實驗發現如果以冷開水沖泡綠茶20~30分鐘，咖啡因的溶出量雖略多於沖泡2分鐘的熱茶，但各種兒茶素的溶出量卻遠高之，尤其置放至隔夜茶液成分仍無氧化現象。
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.
生生不息-正五邊形的繁衍法則
This study was to explore the nature of two basic constitutes of the regular pentagon,With these two constitutes, the regular pentagon could be multiplied into any times. We used four multiplication methods (m2 = 2m1 + n1 、n2 = m1 + n1 、m2= k2m1 、n2= k2n1、a2 = a1 + 1、a2 = a1 + ) to show how the regular pentagon could enlarge and to verify that the enlarged regular pentagons derived from computer did exist. By integrating these four multiplication methods, we were able to arrange regular pentagon of any length of side, and evidenced the equation was
( If the side length of a regular pentagon is a form of m,n is the number of A,B respectively )
We further proved that the first multiplication method could be developed into a new modified method, which could divide a regular pentagon with a given side length into a combination of A and B. But only when the x and y of side length of a regular pentagon could be divided by a natural number, k, and made x/k into an item of the Fibonacci Sequence and y/k a successive item.
When we tried to verify if any regular pentagon could be constituted by other smaller regular pentagons, we also found that it was un-dividable only if the length of pentagon side were ( the number of A, B were the 2n and 2n-1 item of Lucas Sequence). Otherwise, any regular pentagon might be able to be constituted by other smaller regular pentagons.
本研究是以正五邊形的兩個基本組成元素(B)作為討論對象，利用此二元素可以將正五邊形做任意倍數的放大。我們共使用4種繁殖法則(m2 = 2m1 + n1 、n2 = m1 + n1 、m2= k2m1 、n2= k2n1、a2 = a1 + 1、a2 = a1 + ) 來說明正五邊形的放大情形，並利用此4 種繁殖法驗證電腦運算出的放大圖形確實存在。利用這4 種繁殖法則的改良與整合，已達到能排出任意邊長之正五邊形的目標，並能計算並證明出其通式為。
(若正五邊形的邊長為形式,m、n代表、的個數)
更特別的是，我們能用第一繁殖法反推出一種方法，將給定邊長的正五邊形利用簡單的切割方式分成由A、B 組合成的形式，但只有正五邊形邊長之x、y 值可同除以任一自然數k 而使 x/k 為費波那契數列之一項且 y/k 為其後一項者才可以使用。
將此想法推廣至一個正五邊形能否由比他小的其他五邊形組合而成時，我們也發現當正五邊形之邊長為時（其A、B 個數為盧卡斯數列之第2n,2n-1 項），不可分解，否則應該皆可將一個正五邊形分解成比它小的其他五邊形組合（我們也可以利用這些質形檢驗出其他正五邊形是否也為質形）。但其分解形式，不只一種，而我們推測只用兩種較小的正五邊形就能達成，我們期待能找出一或多種分解方法，能將正五邊形分解成標準的分解形式。
線蟲補捉菌Arthrobotrys musiformis 黏液相關基因之選殖與功能界定
線蟲捕捉菌Arthrobotrys musiformis 是一種可經線蟲誘導產生捕捉網來捕捉線蟲的真菌，本實驗即針對A. musiformis 的捕捉網黏液相關基因：Manosyltransferase（AH73）, β-1,3-glucan transferase（AH102）, fimbrin（AH121）及mannose-specific lectin precursor（AH338）進行選殖與功能界定，希望建立這方面的研究基礎，將來能應用在松材線蟲的生物防治上。首先我們大量培養A. musiformis，萃取菌絲體的DNA；接著進行聚合?連鎖反應 (Polymerase Chain Reaction，PCR) ，利用專一性引子對 (primer) 大量增幅AH73、AH102、AH121 及AH338之基因片段；增幅後的產物經過純化、選殖，定序並進行分析比對，確認增幅之序列無誤後，以 Digoxigenin (DIG) 標示當為探針，篩檢A. musiformis 的Fosmid Library﹔目前已成功選殖出AH73 之可能基因，完成AH73 之探針製備，並以其篩檢A. musiformis 的Fosmid Library﹔呈雜合正反應之選殖株 (clones) 將以散彈槍方法（shotgun）定序，作序列組合，探索相關的基因；接下來用 Rapid Amplification of cDNA Ends（RACE) 做出互補DNA (complementary DNA , cDNA) 全長度後；最後建構基因缺失株，驗證此基因所調控的生理以及生化機能。 Nematode trapping fungus Arthrobotrys musiformis can capture nematodes by producing adhesive nets when nematodes go through. Many kinds of nematodes, including pine wood nematode (Bursaphelencus xylophilus), can be captured. Pine wood nematode causes serious pine wood disease. Therefore, A. musiformis has the potential of biocontrol in pine wood nematode. Our research focused on adhesion and adhesive relevant genes of A. musiformis ：Manosyltransferase (AH73), β-1,3-glucan transferase (AH102), fimbrin (AH121), and mannose-specific lectin precursor (AH338). We try to clone these genes and carry out functional analysis. In order to achieve this goal, we used specific primers derived from previously obtained complementary DNA (cDNA), by Polymerase Chain Reaction (PCR) to amplify these genes and gained adequate quantity of genomic DNA products. After sequencing and verifying of the identity of the genomic DNA, we use Digoxigenin （DIG） to label them and use them as probes to screen the constructed A. musiformis Fosmid Library. Currently, the Southern colony hybridization is undergoing. The positive Fosmid clones against the specific probes will be sequenced completely by shotgun library to monitor the existence of adhesion related gene cluster. After working out the full length cDNA of these genes, we will use them to construct replacement vectors to knockout the adhesion related genes, creating mutants and further verify their functions through genotype or phenotype bioassay.
巨型小翼效應—未來長程客機經濟省油妙方
本研究主要是探討翼端小翼對飛機飛行的影響，翼端小翼在現在不少的飛機上都有這種設計，假設小翼可以阻止飛機機翼末端的氣流上旋，進而增加升力與推力，讓飛機能提高飛行時的效率，為了驗證這個假設，因此製作了簡易風洞對小翼的升力與阻力進行定性和定量的探討。升力與阻力的定性定量探討是經由10 組主機翼與五個小翼組合，共有2000 次的測試記錄，再轉化成折線圖予以比較研究，而得到一個穩定性數值結果。這測試實驗的數值結果顯示：小翼可以增加升力，但是也會增加阻力，為了降低阻力，小翼的剖面最好是有弧度。The purpose of this research is to find out the effect resulted from the winglet of the plane to the flight. Many a winglet is nowadays designed for the airplane. Assumes the winglet can stop the air of the tail section of the airplane to revolve up, further increase the force of the raise and the push, and uplift the efficiency of the flight. In order to proof this assumption is correct, so makes an easy air hole to do the research of qualitative and quantitative analysis for the force of the raise and resistance. After about 2000 records tested through the combination of ten sets of the main wing and five tiny wings, and transference of curve diagram , we get a steadily value result. This test result appear the first the winglet can increase the force of the raise, and so do the resistance, and the second to have the force of the resistance decreased, it might be better the section of the winglet is not straight but circular.
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.
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.
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.