所謂約瑟夫問題，就是有 n 個自然數排成一環狀，從頭開始，殺 1(個數)留 1(個數)，求最後留下的數會是多少？該問題在台灣的全國中小學科學展覽出現多次（如表二）。而資訊界演算法大師 Donlad E. Knuth 在其著作 The Art of Programing，CONCRETE MATHEMATICS（具體數學），針對該數列作詳細的說明；但是，不論是歷屆科學展覽或是大師著作，對於該問題，都只是談及殺 1 留β或是殺α留 1。筆者本研究中利用獨創α分類、n 及 k 分類、F 函數、b 函數及循環節，將約瑟夫問題探討範圍提升至殺α(個數)留β(個數)，求倒數第 k 個留下的數是多少？

Table tennis the fastest ball sport in the world has become so fast that rallies have become\r very short. My investigation this year is a further study into slowing the game down. Last\r year I studied the effects the newly introduced 2mm larger ball had on the game. I\r concluded an average increase in rally length from 2.93 to 3.47 balls per rally passing the\r net. Although a 16% increase sounds large, it was an average of less than 1 ball per rally\r difference. I came up with another way to slow the game down my aim was to find out if\r increasing a table tennis net height will decrease spin, speed and increase control i.e. rally\r length and to find out what percentage extent each height level has on these factors. I\r wanted to be able to present a finding as to the optimum net height for the percentage\r increase in rally length that is desired.

(一)內錐孔傳統之量測方法： 利用兩直徑不同之鋼球置於錐孔內而測出兩球之中心距離，計算出半角(Sinθ/2)之值再求正切(Tanθ/2)函數乘以2即得： 兩球中心距 c=h-d1/2+d2/2=[2h-(d1-d2)]/2 兩球半徑差 a=d1/2-d2/2=(d1-d2)/2 Sinθ/2=a/c=[(d1-d2)/2]/{[2-(d1-d2)]/2}=(d1-d2)/[2h-(d1-d2)] (二)以上測量時須使用l.平板 2.鋼球 3.高度規 4.深度分厘卡等綜合如下。 1. 需較多之量具。 2. 測量手續繁多費時。 3. 須經計算。 且在工作進行中無怯量測須待工作完成時才能量測。

The purpose of the study was to develop and create a semi-automatic multi-purpose sorting and counting machine of standard articles. Currently, there is a problem of equipping industrial enterprises as well as small trade companies and large retailers with computing sorting machines of standard products of a certain shape. We would like to fill this missing link up with a simple, compact and inexpensive device. Procedures The proposed research consisted of a consistent design of a virtual model of the device and its electronic-mechanical implementation. The virtual model is simulated by a computer program "SolidWorks" object, which graphically shows the operation of the future device. In the development of the computing sorting device standard electronic devices and their associated software have been used. The created simplified real model demonstrates the basic principles and characteristics of the proposed device. Data As an example for the implementation of the concept device a computing device for sorting coins, in circulation in Russia has been created. As a basic principle of sorting objects by their geometric and weight characteristics were used. It is important that the device is focused on the correct form of the objects of sorting (balls, rings, coins, regular polyhedrons, screws, nuts, etc). To confirm the effectiveness of the computing device of this type of sorting, a series of tests of counting of objects manually have been carried out . The effectiveness of the device is determined by comparing the time characteristics of manual and automatic sorting. Findings and conclusions As a result of research and work performed, we have concluded that: 1) The proposed device can be used in various industries. (for example, while sorting ball bearings.) 2) Such a computing sorting device may find it's application in various commercial enterprises: to assist cashiers in retail ATMs. 3) Can be used in payment terminals. 4) 4) After a certain modernization of the device it can be used for money encashment.

This research primarily aims to observe how does the electric work, why does it work and the relationship between the surrounding circumstance and the repulsive torque. The electric whirl is made of an enameled wire bent into right angle with sharpened ends. When an AC high voltage is applied, the electric field intensity around the whirl ends is strong due to the small curvature radius of the ends. The molecules in air at both ends are ionized. This cause the phenomenon of point discharge. The positive and negative ions produced by alternating current forms AC ion wind, and produce a torque to make the whirl rotate. The object of this experiment is to observe the relationship between the surrounding circumstance and the torque repulsion. We design an apparatus to measure the angular velocity of the rotating whirl. We also calculated the kinetic energy of the whirl and the work done by the torque. The repulsive torque can be obtained by Work energy theorem. Result: (1)The angular velocity of the electric whirl is direct ratio to repulsive torque. When we want to find out the relationship between the manipulate reason and the repulsive torque, we can just compare the angular velocity with the manipulate reason. (2)The angular velocity of the electric whirl is only related to the peak voltage, and it does not make difference whether we apply AC high voltage and DC high voltage. (3)When the humidity is over 68%, the electric whirl cannot function normally. (4)Under the low-pressure circumstance, the electric whirl will rotate with glow discharge and the angular velocity will decrease to zero gradually.本實驗是探討電離轉輪的性質、原理與周圍環境的關係。「電離轉輪」為漆包線兩端折成直角並磨尖而成，接上交流高壓電源時，其尖端曲率半徑小，電場強度相對大，會游離尖端附近的空氣分子，產生尖端放電的現象，而交流電交替產生的正、負離子會形成交流離子風，並產生轉動力矩，使轉輪轉動。我們設計一個裝置，使其能偵測轉輪轉動的狀況，運用測得數據計算出轉動時的動能和作功狀況，套用功能定理便可求得轉輪通電時產生的斥力矩。實驗結果顯示(1)轉輪的角速度和尖端斥力矩成正相關，所以當我們想得知尖端斥力矩和實驗操縱變因的關係時，只要比較角速度和操縱變因就可以了，這簡化了原本繁複的計算和冗長的數據處理過程。(2)轉輪的角速度只和峰值電壓有關，和直流或交流沒有直接關係。(3)轉輪在超過溼度68%之後，就不會正常運作。(4)在低壓條件下，轉輪轉動時會伴隨淡紫色的輝光放電(glow discharge)現象，而抽氣塔中與轉輪尖端最接近的一點，也就是電場最強的一點，會和尖端同時產生光芒，相互輝映。

We operated the misexpression screen between the EP lines and the pattern lines with the genotypes of eq1>dll, eq1>abdA, eq1>Ubx, eq1-GAL4, ey-GAL4 or dpp-GAL4. After the screening, we found that five of these 1,800 strains of filial generation had special phenotypes. It had shorter antennae and defects in the anterior equatorial region of eyes. We used plasmid rescue and IPCR to sequence the certain target gene, and found that it was escargot, abbreviated as esg. To identify when, where and how the overexpression of escargot induces such phenotype, we operated the staining of eye-antenna disc in third-instar larval period of wild type, eq> esg×UAS-GFP and eq>GFP with anti-dll, anti-caspase3 and anti-esg. The result shows that escargot cannot be detected before puparium formation. But the expression of dll, a gene controls the eye development, was reduced in the eye disc. We except the overexpression cause the defect of distal antennae and the anterior equatorial region of eyes mainly in the 3-day-long pupal life.我們用異位表現法篩選出和eq1>dll、eq1>abdA、eq1>Ubx、eq1-GAL4、ey-GAL4或dpp-GAL4 這些pattern lines有交互作用的EP lines。在這1800種的果蠅子代品系中，有五種具有特殊的性 狀。它們具有觸角短化以及複眼前緣中央區有缺刻的現象(形成心型眼)。我們使用質體救援 法以及IPCR的方法來定序這段未知基因序列，發現這是一個叫做escargot的基因(簡稱esg)。 為了了解過分表現此基因會造成何種分子影響，以至於產生此種性狀，因此我們使用 anti-dll 、anti-caspase3 和anti-esg 進行野生型、eq>esg×UAS-GFP 和eq>GFP 三齡幼蟲的 eye-antenna disc的螢光免疫染色。結果在幼蟲成蛹前都沒有偵測到esg的表現現象；不過在eye disc中，控制眼睛發育的基因dll的表現有被抑制的現象。因此我們推測過分表現esg的過程因 該是發生在為其短短三天的蛹期。也就是說，這種表型應該是在化蛹後形成。

地震波會以橫波和縱波的方式傳遞能量，學校的教學大樓中地下具有蓄水池者搖晃的持續性感覺比較短暫，於是利用彈簧波模擬地震波測試不同質量的台車接收到的能量會較空車為多。並利用自製模型測試不同容器形狀和水量的阻尼作用，結果發現搖擺時，時間球形＞錐形台≒方形台；球形台裝有不同水量時擺動時間裝滿裝滿時＞未裝水＞裝1500mL 時；平行移動時則是球形台裝水2000mL 後鉛錘移動距離最短。整個實驗過程中由於未裝滿水的模型內部重心改變不規律，而且模型內所裝的水量因為不規則擾動經吸收的能量轉換成水溫上升的熱能，因此導致擺動能量的消耗造成擺動時間縮短，如果新式大樓興建時考慮消防蓄水池和水塔的造型和裝水容量，應可以減少地震時的搖晃時間，降低心理的緊張和物體因震動而產生的移動傷害。Seismic wave can transmit energy with transverse and longitudinal wave. The shaking of these buildings with reservoirs underground in our school for a shorter time, so we use spring wave to simulate seismic wave, and test the proportion of transmissible energy received from different mass of objects. The energy gets from wave motion passing on is bigger when cars carrying capacity than empty cars. And we use homemade models to test damped effect of different forms and water. At last we discover the time is Sphere ＞ Taper ≒ Square while they swing with different amounts of water, the time it cost is Full ＞ Non ＞ 1500 mL. When they move horizontally, the plummet moved shortest, when the water of the sphere is 2000 mL. During the whole experiment, the center of gravity in the models, which are not full of water changes irregularly, and the water in the models can absorb heat energy from energy disturbing, so the swing of energy consuming makes the time of the swing shorter. If the fire controls reservoirs, the shapes and dress up water volume of the water towers, are taken into consideration, the duration of the shaking of earthquake will be shortened so that our fear and nervousness will be lessened, and the damage causer from the shaking will be reduced.

The zebrafish (Danio rerio) is a popular model organism used for elucidating complex\r developmental pathways and processes. Although the Zebrafish Genome Project is\r nearing completion, the function of most genes remains to be discovered. In zebrafish,\r where an efficient gene targeting method is still absent, costly Morpholinos (MOs) have\r been widely used to ‘knockdown’ specific genes.

Marsilea quadrifolia, an aquatic perennial rhizomatous fern, is widespread on wetlands in Taiwan. A normal fern frond has the clusters of spore capsules on the back, yet Marsilea quadrifolia reproduces clusters at petiole base from sporocarps which are axillary, pedicellate, ovate and hairy; both microsporangia and megasporangia can be found in sporocarps. It is highly polymorphic. The sterile fronds are erect when growing in mud, and floating in water, and they produce leaflets in the shape of four-leaf clovers. Mature leaves are divided into water leaves and terrestrial leaves according to living environments. Water leaves are divided into submerged leaves, floating leaves, and emergent leaves. These four kinds of leaves have obvious differences in stoma density. The submerged leaves have the least starch which means they have the minimum photosynthetic efficiency. The flexible leafstalks allow the plants to adapt to small changes in water level, while keeping their leaves on the water surface to access light and carbon dioxide. Thus, heterophylly may be seen as an adaptive mechanism which is sensitive to some environmental parameters and that responds accordingly to maximize the capability for survival. The terrestrial leaves have periodic sleep movement according to the alternate changes of day and night. The biggest opening angle is related to a definite leaf closing time cycle. Light interference during the dark period, continuous lighting, or the reversing of day and night all interfere the opening time and speed of them.南國田字草是一種浮葉性、多年生水生蕨類，匍匐莖細長橫臥在水中泥土或濕地裡，葉四枚對生於葉柄頂端，依生長環境不同，可分為水生葉及陸生葉，水生葉又分沉水葉、浮水葉及挺水葉三種。孢子囊群聚集特化成堅硬的孢子囊果，長於葉柄基部，孢子有大、小孢子兩型。四種異型葉在內部構造、氣孔分布密度上皆有相當的差異，以適應環境的變化，葉片澱粉含量以沉水葉最少。南國田字草陸生葉隨著晝夜交替，具有週期性的睡眠運動，每天葉片開啟的最大角度和閉合時間有一定的時間範圍。黑暗期受光照干擾或連續照光、日夜顛倒，皆影響葉片的開閉時間與速率。

一、若Mn×n(s)表示在n×n 的正方形棋盤中，排列s 顆棋子在方格內，且每一方格最多只能排1子，其中s 顆棋子的配置需滿足兩個條件：1. 並無任意4 子可以形成矩形框的4 個頂點。（此矩形框的邊需與棋盤的邊平行）2. 在沒有棋子的方格中，無法再加入棋子。二、若Vn×n×n(a1,……,an) 表示在n×n×n 的正方體棋盤中，每層的棋子個數分別為a1,……,an，且s= a1+……+an，其中s 顆棋子的配置需滿足兩個條件：1. 並無任意8 子可以形成長方體的8 個頂點。（此長方體的邊需與立體棋盤的邊平行）2. 在沒有棋子的方格中，無法再加入棋子。本研究即在Mn×n(s)與Vn×n×n(a1,……,an) , s= a1+……+an 中探討s 的最小值、最大值及變化情形，並分析其配置方法。之後推廣至長方形Mn×m(s)及長方體Vn×m×k(a1,……,ak) , s= a1+……+ak。最後根據其研究結果設計一個「避開矩形框棋」，並加以分析出致勝的策略。一．If Mn×n(s) indicates in the n×n square chessboard, we put s chesses to line in the square and each square only can put one chess. Then the station of s chesses must satisfy the following two conditions：1. No any 4 chesses can form the tops of the rectangular frame ( The sides of rectangular frame must be parallel to the sides of chessboard )2. If there’s no chess in the square, we can’t add any chess. 二．If Mn×n×n(a1,……,an) indicates in the n×n×n square chessboard, the chess number in each layer are a1,……,an and s= a1+……+an. The station of s chesses must satisfy the following two conditions： 1. No any 8 chesses can form eight tops of the rectangular cube ( The sides of rectangular cube must be parallel to the sides of cubic chessboard ) 2. If there’s no chess in the square, we can’t add any chess. This research try to explore the minimum, maximum and variation of s which in Mn×n(s) and Mn×n×n(a1,……,an), s= a1+……+an, and analyze its station. Then we will extend the research to rectangle Mn×m(s) and rectangular cube Vn×m×k(a1,……,ak), s= a1+……+ak. Finally, according to the result of research we wish can design one “avert rectangular frame chess“ and analyze the strategies to triumph.

本實驗主要探討具異形葉性的植物－異葉水蓑衣(Hygrophila difformis)異形葉的變化和\r 不同環境因子測定之下的關係，我們利用光度、光質、二氧化碳、交換水陸環境、噴灑Ethephon\r 的不同環境因子來觀察異形葉的變化。我們以水陸生植株的各項特徵(葉形缺刻、葉綠素a/b\r 比值)當作標準值，發現高光度及在水中通入二氧化碳會使植株葉形趨向陸生葉，將水生植株\r 去淹水也得到相同的結果，而將陸生植株淹水在本實驗測定時間(28 天)中並未發現葉形有明顯\r 變化，對陸生葉噴灑Ethephon 使植株產生乙烯，並增加陸生葉氣孔的數量，但在異形葉的形\r 成上並無明顯影響。由本實驗各項結果看來異葉水蓑衣的異形葉的確會因為環境的改變，調整\r 葉形及生理特徵，使其在所處的環境之下能夠達到最好的適應。

秀麗隱桿線蟲(Caenorhabditis elegans)為在科學界備受矚目的模式生物，對於其生殖及發育過程已有諸多研究，然而對於其覓食及攝食行為的相關研究卻仍闕如；每一種生物都有其獨特的行為模式，而為了解線蟲發展出何種覓食與攝食的行為以適應自然的環境，因此著手進行研究。本研究歸納出線蟲的七種一般行為：前進、探頭、偏移、擺頭、後退、轉向及拐彎行為，並探討其意義。其中，前進及探頭行為為恆常出現。偏移與轉向行為與攝食有關，在有菌環境中出現，可避免其遠離食物來源，而連續的後退及轉向行為也構成特殊行為之樹枝狀行為，推測應為幫助線蟲的消化所出現的行為。擺頭與拐彎行為與覓食有關，在無菌環境中出現。後退行為雖在有無菌環境中皆出現，但由後退後行為的不同可以了解後退行為在兩種環境下具有不同意義。在有菌環境中，後退後通常伴隨轉向行為；在無菌環境中，後退後通常伴隨拐彎行為，為逃離不適環境且藉以覓食的行為。經過研究，發現線蟲的覓食機制為嗅覺，且對嗅覺有依賴性及專一性，在其他氣味存在的環境下會大大降低覓食的效率，但最後仍然能正確地找到食物來源。線蟲於覓食的過程中所出現的特殊行為之混亂行為，由實驗結果發現為是E. coli 所釋放至培養基的化學物質所造成，化學物質濃度越濃，線蟲所表現出的混亂行為就越明顯。推測此種現象發生的原因，應為E. coli 釋放化學物質以干擾線蟲，以避免本身受到捕食，然而，線蟲也演化出適應的能力，因此在發生混亂行為後仍然能抵達菌落，此種特殊的交互作用表現出線蟲與E. coli 間的共演化現象。Cenorhabditis elegans has long been a model organism used for developmental biology studies. However, researches about its foraging and feeding behaviors are still limited. Every organism has its unique behaviors, and this research was conducted in order to understand more on what kind of foraging and feeding behaviors were developed by C. elegans and how they helped C. elegans to adapt to the environment in which it lives. The research concluded with seven general behaviors of C. elegans : advancing, probing, slanting, swaying, backing, turning and bending, and the meanings of it. The advancing and probing behaviors are constant. The slanting and turning behaviors, which appear in presence of food, are feeding-associated behaviors, which help C. elegans avoid leaving the food source. Continuous backing and turning behaviors also make up the branching behavior, one of the special behaviors, which help C. elegans’ digestion. Swaying and bending behaviors, which appear in absence of food, are foraging-associated behaviors. Although backing behavior appear both in presence and absence of food, the difference in post-backing behaviors show that there are distinct meanings of backing behavior in each environment. In presence of food, turning after backing is usually observed; in absence of food, bending after backing is usually observed, which indicates the act of escaping from unsuitable environment and searching for food. Studies show that the foraging mechanism of C. elegans is by olfaction, and C. elegans is highly olfaction-dependent and specific: efficiency of foraging decreases significantly under environment with scents other than that of E. coli, but C. elegans is still able to locate the food. According the experiments, the chaos behavior, one of the special behaviors, appears during the foraging process of C. elegans, and is caused by chemicals released to the medium by E. coli. The density of the chemicals and the extent of chaos behavior is in direct proportion. The theory is E. coli secrets chemicals to disturb the worm to avoid being preyed upon. C. elegans, however, also evolved the ability to adapt to the chemical so that it can still reaches the food source even after chaos behavior appeared. This unique interaction is a manifestation of co-evolution between C. elegans and E. coli.