臺灣

We consider a game played with chips on a strip of squares. The squares are labeled, left to right, with 1, 2, 3, . . ., and there are k chips initially placed on distinct squares. Two players take turns to move one of these chips to the next empty square to its left. In this project, we study four different games according to the following \r rules: Game A: the player who places a chip on square 1 wins;Game B: the player who places a chip on square 1 loses;Game C: the player who finishes up with chips on 12 . . . k wins;Game D: the player who finishes up with chips on 12 . . . k loses. After studying the cases k = 3, 4,5 and 6 for Game A and the relation among these four games, we are led to discover the winning strategy of each game for any positive integer k. The strategies of Games A, B and C are closely related through a forward or backward shifting in position. We also found that such strategies are similar to the type of Nim game that awards the player taking the last chip. Game D is totally different from the rest. To solve this game, we investigate the Nim game that declares the player taking the last chips loser. Amazingly, the strategies of two Nim games can be concisely linked by two equations. Through these two Nim games, we not only find the winning strategy of Game D but also the precise relation between Game D and all others.\r 去年我研究一個遊戲：有一列n個的方格中，從左至右依序編號為1,2,3,....n。在X1個、第X2個、第X3個格子中各放置一個棋子。甲乙二個人按照下列規則輪流移動棋子：\r 一、甲乙兩個人每次只能動一個棋子(三個棋子中任選一個)。遊戲開始由甲先移動動棋子。二、甲乙兩個人每次移動某一個棋子時，只能將這個棋子移至左邊最近的空格(若前面連續有P個棋時可以跳過前面的P個棋子而且只能跳一次)，而且每個方格中最多只能放一個棋子。\r 研究這個遊戲問題時，我討論四種不同"輸贏結果"的規定：甲乙兩個人中，A誰先將三個棋子中任意一個棋子移到第一個方格，誰就是贏家。B誰先將三個棋子中任意一個棋子移到第一個方格，誰就是輸家。C誰先不能再移動任何棋子，誰就是輸家。D誰先不能再移動任何棋子，誰就是贏家。\r 當"輸贏結果"的規定採用ABCD時─我們稱為遊戲ABCD。今年我將把這個遊戲問題中棋子的個數由三個推廣到一般K個情形之後，再繼續研究遊戲的致勝策略，同時也將研究遊戲ABCD之間的關係。

現今乳酸菌飲料風行，但是乳酸菌是否真能通過胃酸的考驗，到達腸道進行複製，利益人體？我們首先以市售乳酸菌粉（加拿大Rosell 公司，含二種菌，暫時命名為"小毛"及"小白"）為預測菌種，利用分光光度計測定乳酸菌於Thioglycollate 培養基中的生長能力（OD600）。小毛在pH 值 1、 3 、5、 7 時之生長力分別為0、 0.008 、0.682 、0.847 ，小白為 0、 0.015 、0.973、 0.636。若於培養基中添加不同濃度的螺旋藻熱分解物，如加入0.01%的添加物後，小毛在以上各種pH 值生長力分別為0.042、1.291, 、1.447, 、1.213 ，小白為 0.053、1.392、 1.531、 0.988，意外發現可大幅提升菌的生長力及抗酸力。再取台灣市售4 種廠牌優酪乳（以甲、乙、丙、丁代表之），分離乳酸菌，再於各種pH 值中培養。結果在pH 3 時，螺旋藻熱分解物僅對丙廠牌有效, 乙廠牌無效, 甲與丙則有無填加生長力都很差。在pH 1 時, 則對乙、丙、丁皆有效，故建議廠商慎選菌種，並於製程及成品中添加螺旋藻熱分解物。The yogurt is a popular drink. But whether the lactobacilli inside can resist the destruction of gastric acid and grow well in the intestinal tract is still questionable. We used pure lactobacilli powder (Rosell Company, Canada, containing two bacteria named in this report as "Little Hair" and "Small White") for pre-test. The growth ability in thioglycollate medium was determined by spectrophotometer (OD600). The results of bacterial growth at pH 1, 3, 5, and 7 for "Little Hair" were 0, 0.008, 0.682, and 0.847, respectively. Those for "Small White" were 0, 0.015, 0.973, and 0.636, respectively. After supplement with 0.01% of the boiled lysate of Spirulina algae (ProBio Biotech, Taiwan), growth abilities at pH 1, 3, 5, and 7 for "Little Hair" were 0.042, 1.292, 1.447, and 1.213, respectively. Those for "Small White" were 0.053, 1.392, 1.531, and 0.988, respectively. The algae extract amply promotes the growth and acid-resistance, especially at pH 3, of these bacteria. The lactobacilli isolated from four different products of yogurt in Taiwan, named as A, B, C, and D, were then tested as above. Results showed the supplement with the boiled lysate of Spirulina algae was very effective, at pH 3, for promoting growth of C, but not effective for B. Growth abilities of both A and D were very unsatisfactory with or without this supplement. At pH 1, algae lysate supplement significantly improved the growths of B, C, and D. Therefore, this supplement in culture and product for yogurt preparation was suggested.

花青素具抗氧化的能力，我們想了解植物生長時，可見光中不同色光照射與花青素生成多寡是否有關，所以本實驗以不同波長的LED照射紫莖蘿蔔嬰、紫高麗菜芽、紅鳳菜，探討花青素含量與色光的關係。利用花青素具有抗氧化的特性，以碘滴定和自製鐵粉片生鏽面積的方法，檢測含花青素水溶液的抗氧化力，推論花青素的含量。結果發現：可見光的波長愈短，植物抗氧化能力愈好，因此推論紫光照射，可增加植物花青素量。而在不同光照強度影響花青素含量實驗結果發現：各種色光距離愈近，抗氧化能力愈好，花青素愈多，但紫光照射芽菜距離少於15公分時，抗氧化力轉差，推論若短波紫光能量太強，會導致破壞，不利花青素生成。

直接乙醇燃料電池以酒精與氧氣透過氧化還原反應產生電能，但化學反應緩慢，需利用觸媒以增加其速率。本實驗目的在於盡可能找出一個表現最佳的觸媒。本實驗利用活性碳粉作為觸媒（鉑、錫）的載體，以酸性（HNO3）與鹼性（NaOH）環境分別處理碳粉，再以含浸法與多元醇含浸法將觸媒還原。我們得到以HNO3 處理的碳粉無法保有原碳粉的型態，較利用NaOH 處理為差。在觸媒製備方面，多元醇含浸法還原效果比含浸法可得到較小的觸媒尺寸，在本實驗中，溶液中鉑與加入的碳粉重量比為3:7 時，可得到最大的反應面積。此外，當鉑與錫原子數比為4:1 時，可得到最大的乙醇氧化電流。Direct ethanol fuel cell is a kind of power source which generates electrical power by a redox reaction involving ethanol fuel and oxygen. However, this reaction takes place slowly; therefore, catalyst is needed to improve its activity. The goal of this project is to get an optimize catalysts ratio to obtain the best catalyst activity. Activated carbon is used as the support of catalyst (platinum and tin) particles in this project, which is pre-treated in acid (HNO3) and alkaline (NaOH) solutions respectively. Then, the precursor is reduced by impregnation and EG-impregnation. We learned that activated carbon pre-treated with NaOH activates better than which pre-treated with HNO3 because the latter bear less resemblance than the former. As for the catalyst, the results of EG-impregnation show smaller size of catalyst particles than those of impregnation. In this project, when the ratio of the weight of platinum and activated carbon added into the solution is 3:7, we can get the largest surface area. In addition, when the ratio of the amount of platinum and tin atoms is 4:1, we can get the largest current of ethanol oxidation.

目前生物學知識認為雉科鳥類的性別，在卵受精後即決定(WZ型)，不受環境的影響，但是在本組一連串的實驗中發現，雉科鳥類的性別與孵化的溫度變化有非常大的影響，一般宮廷雞的孵化條件在濕度55％RH及溫度98℉～99℉，在此孵化條件下宮廷雞的子代♀：♂=1：1，若溫度降為97℉的孵化條件下所得子代♀性佔93％，倘若溫度升高為100℉的孵化條件下所得子代♂性佔92％，可見在比正常孵化溫度高的環境下宮廷雞的受精卵會轉變為♂性，而比正常孵化溫度低的環境下孵化的宮廷雞受精卵卻會轉變為♀性，本實驗續做了六代，結果大致相似，由此可以證明控制孵化溫度可以改變宮廷雞的性別，這一行為，可能與Z染色體上一個溫度依賴型的連鎖基因(DMRT1)之表現有關。 ;The temperature of hatching can affect Chinese silkys's sex It is now established that the sex of Pheasants is determined when the egg is impregnated, rather than by environmental factors. However, in a series of experiments, we find that the sex of Pheasants is strongly related to the temperature of hatching. In the normal hatching condition (humidity:55% RH ,temperature: 98.5℉), the ratio of female and male offspring of Chinese silkys is 1:1. If the temperature is lowered to 97℉, the female offspring occupies a proportion of 93%. If the temperature is raised to 100℉, the male proportion will reach 92%. We can thus derive the conclusion: the impregnated eggs of Chinese silkys will be transformed to male at a temperature higher than the normal one, while a lower temperature than the normal one will cause the impregnated eggs to be female. The experiments have been conducted through six generations of Chinese silkys, and the results are practically the same. This indicates that temperature changes can affect gender, This may be related to a Z-linked of DMRT1 gene on the DNA, which is temperature-dependent.

本研究關注酵母菌與食糖的發酵作用，並設計簡易測量產氣量的裝置。實驗結果發現： 1. 多醣(果寡糖)、雙醣(黑糖、蔗糖、冰糖)發酵速度比單醣(葡萄糖、果醣)快。 2. 冰糖、黑糖、葡萄糖產氣量中顆粒＞細顆粒，蔗糖無明顯差異。 3. 無封口產氣量多，有封口前20分鐘不穩定。產氣量穩定度為：G型發酵管＞U型發酵管＞市售發酵管。 4. 自製U型發酵管左右數值平均，總產量比發酵管少3mL。 5. 自製G型發酵管左側產氣量多，兩側產氣量接近市售發酵管。 6. 自製排水集氣發酵瓶產氣量，總產量比發酵瓶多1mL。 7. 食糖濃度低，產氣量多、時間快；濃度高，產氣量少、時間慢。 8. 麵粉濃度高，產氣量多、時間快。 9. 食糖和麵粉濃度高，30分鐘後有二次發酵的情形。

演奏樂器時，是使發聲體產生駐波而發出各式各樣悠揚的聲音及音調；樂器主要分成振動體(發聲體)及共鳴器兩部分，依發音方式分為弦樂器(使弦振動產生駐波)、管樂器(利用空氣柱振動產生駐波) 及打擊樂器(利用板、膜或磚等彈性材料的固有頻率振動產生駐波)。聲音有三要素：振幅、頻率及波型，響度取決於振幅大小、音調與頻率有關、波型則由不同的頻率及響度組成。樂音多變的主因是音色及音調。音色是發聲體的發音特性，取決於該發聲體的聲波波型。音調即聲音的高低，與發聲體的振動頻率材質息息相關，頻率愈高，其音調愈高，而樂曲中的音階高低則是由音調高低所構成。樂曲的製作及演奏必涉及到律制，從駐波的產生、律制的探討、頻率的測量和琴鍵的振動模型建立與波形的觀察，我們使用計頻器、示波器及有限元素ANSYS 軟體、數學計算Mathematica 軟體，我們設計一系列實驗，企圖對樂器聲波操作技巧有更進一步的認知。從實地走訪樂器製造廠，了解到設計與改良仍是樂器工藝家重要課題，本文的實驗方法可提供大型演奏會現場調音、樂器調音師或樂器工藝家設計製造樂器時參考用，對於發展文化產業期待提供更經濟與實用的建議。;Playing musical instrument is to make sounding part produce stationary wave so as to give off various gentle sounds and tones. According to different modes of sound producing, musical instruments which comprise vibrator (sounding part) and resonator can be divided into stringed instruments (which vibrate the strings to produce stationary wave), wind instruments (which produce stationary wave with vibration of the air column) and percussion instruments (which produce stationary wave with natural frequency of boards, films or bricks). Three Essentials of sound include amplitude, frequency and waveform, in which the amplitude decides the volume, tones are related to frequency and the waveforms are composed of different frequency and volume. Various musical sounds are mainly due to different timbres and tones. Timbres, sounding characteristics of sounding part, is decided by waveform of the sounding part. Tone means pitch of the sound and is closely related to vibrating frequency of sounding part. Higher frequency makes higher tones and pitch of a musical scale is decided by different tones. Music composing and playing is necessarily connected with music temperament including producing of stationary wave, discussion of temperament, measurement of frequency, establishment of vibrating mode of keys and observation of waveform. We adopted frequency counter, wave inspector, ANSYS software and Mathematica software and designed a series of experiment to get further knowledge of technique of handling musical instrument wave. After visiting musical instrument manufacturers, we learnt that design and improvement are still the essential subjects for instrument craftsmen. Experimental method in his article can provide reference for on-the-spot tuning of large concert, musical instrument tuner and musical instrument designing and manufacturing by craftsmen, and more economic and practical suggestion for cultural industry development.

關於平面上若干點的集中度之定義，一直很少有人予以仔細的探討，因為判別的方法有很多種。本研究是以平面上三點所構成的三角形之三頂點作討論，分別以三角形的面積、周長，內心、外心和重心至三頂點距離，三點的標準差及平均差的概念，作為不同的判別方式，並以動態幾何化版ＧＳＰ模擬不同的判斷方法做為研究，在利用統計學上的方法，找出哪一種定義方式最為適合、誤差最少的判斷方法。There are many ways to determine the centralness of three dots on a plane; however, no definition study has been applied. In this study, we focus our interests on the entralness of three vertices of a triangle formed from three dots on a plane. Various methods such as the relationship of area, and the distance of the triangle to the centralness of three dots, the distance from the interior point, exterior point, the barycenter to the vertices of triangle, and the standard error and differences average obtained from three dots were determined with a dynamic geometry software GSP, and a statistic method was used to find a least error way to determine the centralness of three dots on a plane.

給定一個P∈(0,1),令k0=0, p0=p，定義k1為能使 的最小正整數k，而 ; 相同的，對於給定的kn-1, kn 為能使的最小正整數k, 。若存在kn 使得，則稱p∈ In; 若對於所有n 與kn ，，則稱p∈ I∞。如此區間(0,1)可分解成集合I1,I2,…,I∞。

本研究探討肥皂膜與肥皂水的共振現象。在肥皂膜共振方面，我們以實驗探討皂膜的共 振模式與頻率的關係；並配合共振理論模型求出薄膜厚度，再與體積密度-厚度測量方法比 較。而又發現皂膜在共振時，皂膜保存時間較平常久，故進行皂膜生命期與頻率、強度的關 係。在進行肥皂膜實驗時，肥皂水滴落在喇叭上，振動出奇特的形狀，進而探討皂水共振的 特性並嘗試建立其數學模式。 ;The research is about the resonance of soap film and soapsuds. For the resonante of soap film, we tried to find out the relation between the resonant pattern and frequency by experiment; according to the resonante model, we measured the thickness of soap film, which was compaired with volume-dencity method. We found that the life-time of the resonant soap film is longer than the normal one, so we proceeded to study the relation between the life-time, frequency, and power. We observed special resonant pattern while the soapsuds fell down on the speaker. So we studied the characteristics of resonant soapsuds, trying to make the mathematical pattern of resonant soapsuds.