本研究探討不同因素對冰淇淋的影響，從成分、減少油脂含量、打發鮮奶油著手，並研發簡易測量方法——利用位能、摩擦力等科學概念測量硬度，讓數字客觀地說話，研究製作出步驟簡單、少添加物且低脂的冰淇淋。研究過程中我們對於冰淇淋相關知識，如成分、製作技巧等，以及能量、摩擦力的概念有了更深刻的印象。 利用本實驗結果推算出「冰淇淋函數」，在同油脂量冰淇淋不同溫度下得到對應的硬度(摩擦力)，及最後找出同溫下不同油脂量的冰淇淋所對應的硬度(摩擦力)，可客製化適合不同客群的冰淇淋，並且利用打發鮮奶油時間降低冰淇淋的油脂含量，研發出低脂冰淇淋。

本研究由下述問題開始：將n1 個黑色棋子和n2 個白色棋子排成一列，規定第一個棋子必為黑棋；對於每一種排列方法中，同色棋相鄰處記為1，異色棋相鄰處記為-1，所有1 和-1 的總和記為 t (n1,n2 )。對所有可能的排列方法所算出來的t( n1,n2 ) 值求其平均值，記為a (n1,n2 ) 。我們先由觀察各種n1 和n2 值，得到這平均值的可能公式，隨後並嚴格證明其正確性，證明方法也經過多次精鍊到十分簡潔的方式。以此為基礎，我們並做了各方向的推廣，研究涉及下列各點：(一) 利用組合數探討原來的問題。(二) 在第一個棋子不限定為黑棋的假設下，求平均值a( n1,n2 ) 。(三) 將棋子由兩種增加到多種。(四) 改變棋子排列以及相鄰的方式。經由研究，我們發現，每一次愈將問題推廣時，愈能找出清晰的概念涵蓋並印證先前的想法。Our study starts with the following problem. Suppose n1 black chesses and n2 white chesses are arranged in a line under the condition that the first chess is black. For any arrangement of these chesses, an adjacent pair of chesses having the same (respectively, different) colors is associated with a value of 1 (respectively, -1). Let t(n1,n2 ) denote the sum of these values. The purpose of this problem is to calculate the average value a (n1,n2 ) of these t (n1,n2 )which runs over all possible arrangements of the chesses described above. We begin from observing various values of n1 and n2 and find a possible formula for the solution. We then give a rigorous proof for the formula. After some refinements, simple proofs are also established. Based on this, we also make some generalizations. In summary, the research includes the following: 1. Study the problem by using binomial coefficients. 2. Calculate a(n1,n2 ) when t( n1,n2 ) runs over all possible arrangements in which the first chess can be black or white. 3. Increase the types of chesses from two to many. 4. Variant the arrangement method of the chesses from a line to other configurations. During the study, we find that whenever we extend the problem to a more general case, we make the ideas for the original problem clearer.

在這個科展中我們要研究兩個非常有趣的問題：\r 停車場問題 與 彈硬幣遊戲.\r 停車場問題是這樣的：在一條單行道上有n個車位，編號從1到n。現在有n個司機排成一排要進入停車。但是每個司機都有怪癖，各自有最想要停的位子。他們依序將車子開進單行道，如果想要停的位子是空的，當然停在這個位子。但是如果不巧那個位子已經被停了，不得已只好找下一個空位，姑且停之。但是如果往下找都沒有空位，由於是單行道，司機就只好開走不停了。\r 比如說，如果現在有五輛車，司機的喜好分別是(3,1,2,5,2)。則五輛車都可以順利停車。但是司機的喜好如果是(3,1,4,5,4)，有些車就無法停車了。\r 彈硬幣遊戲是這樣的：考慮圓內接正n+1邊形，任意兩點都連線。這正n+1邊形中有一個頂點P是特殊的，每個頂點上一開始都放有一些硬幣(各點硬幣數可以不同)。如果P以外的某個頂點上的硬幣數n個，我們可以對這個頂點進行操作：一次操作是指將這個頂點上的硬幣各分一個給每個其他頂點。點P只在其他點都無法操作時操作。我們不理會頂點P上的錢數，因此這個遊戲可以無限地玩下去。

本研究首先探討台灣各地的日照時數與世界重要都市的比較，發現台灣南部日照時數皆超過2000 小時，適合發展太陽能。接著，?了增加陽光的能量密度而加設弗瑞奈透鏡，雖然能順利的使照度放大三百餘倍，但歲日照角度的影響甚鉅，?了克服角度的問題，我們決定開發自製的追蹤器來改善角度的問題。太陽能板需要改變仰角跟傾角（雙軸調整），由光感應器判斷及自動控制程式，判斷隨時辰與季節變化的太陽角度。當搭配奈米塗料、弗瑞奈透鏡與追蹤器，總輸出功率可增加約50%。太陽電池表面玻璃會阻擋藍紫光的吸收，但本研究在太陽能板上塗佈奈米塗料，發現能增加短波長的吸收；經實驗後奈米等級表面具有自潔效應，可防止灰塵雨滴的堆積影響光線吸收，具有開發價值。This project first compares Taiwanese locations with other places in the world on average daylight times. It was discovered that southern Taiwan has the longest average daylight time all over 2000 hour sand therefore most ripe for solar power development. To increase the energy density of solar Fresnel lenses were incorporated. Although this has the advantage of magnifying illumination by three hundred percent, the alignment angle for the solar panel will have a significant impact on performance. We then designed and built a automated tracking device with illumination sensors to control the elevation and inclination of the solar panel which adjusts the angle according to environmental conditions such as time of day and season. When solar cell collocate Nano coating, Fresnel lens, tracking device, its power can promote almost150%. The glasses on the solar cell will interfere solar cell absorbing blue and purple light, but we lay on a Nano coating and we find Nano coating can improve solar cell to absorb short wave; and surface o Nano have lotus effect, it can prevent dust and rain effecting solar cell absorb lights, and it is worth developing .

Up to this time we have spent almost three years in studying condensation and water droplets. Little could we have done as compared with the almighty nature. However we are rewarded by the nature as we gradually found the secrets about electro-magneto field and water droplets: The size of water droplets turn smaller upon electro-magneto field and grow more uniformly especially upon electric field. This experiment presented here is actually the diary of the growth of water droplets in condensation, upon magnetic field and electric field. Through convection, it discusses the self assembly patterns of water droplets and peep into the uniformity both of the size and the distribution mode of water droplets. In former basic experiment, we focus on temperature and the speed of water moisture; generally speaking, higher temperature speeds up the coalescence procedure but does not affects the nucleation size of water droplets in simple plain surroundings; while speed of moisture does affects the nucleation size. As we went farther, deep into convection and found magneto-electric force did play an important role in the self assembly mechanism of water droplets. The topic is mostly concerned as we are surrounded by magneto-electric waves in today’s world. This experiment anchors the first step in discovering the uniformity of water droplets in different environment, and providing insights into the self assembly mechanism of water droplets upon electro-magneto field with nano sizes. 這是一系列關於水蒸氣冷凝為極細微小水珠的實驗。其中可以分為兩大部分； 第一部分是基礎實驗。將水蒸氣導入至潔淨的介面上(蓋玻片)，觀察冷凝水珠的結構。雖然看似簡單平常，但卻有令人驚奇的發現；不同溫度的水蒸氣，其冷凝最初始的細微顆粒之尺寸是相同的 ！爾後隨著溫度的升高，堆疊速率也跟著上升；以致於最後一起呈現出來的水珠大小不一，尺寸不一。 第二部分是將水蒸氣導到磁場及靜電場上，觀察其冷凝結構。這部分的實驗推翻了一般「水分子是電中性在電磁場中不受影響？」的刻板觀念 ！實驗所呈現出來的冷凝水珠，不但於附加磁場中尺寸縮小又不易長大，同時還有固定的自我組成模式( Slef-assembly pattern);而且也發現在磁場中的冷凝小水珠的尺寸比電場中的小，可是電場中的小水珠則表現出較大的均勻特質。

本研究主要的目的是在開發同時具有空氣清淨與照明的兩種燈具。其中桌燈是基於自然對流原理，利用燈泡發熱讓氣流通過燈具上方的濾網達到過濾功能，為了尋求過濾效果與照度兼顧的最佳值，本研究並提出比較因子的概念。在吊燈方面，除了運用自然對流原理之外，還更進一步利用太陽能驅動風扇，進行強制對流，強化過濾的效果，使得本研究成果更趨於完善。 由實驗結果可得知，桌燈在四星期長期測試條件之下，其過濾效果增進率分別為39.1, 40.8與 40.1%。在吊燈四週長期實驗的結果方面，螺旋與 100W 鎢絲燈泡在自然對流的過濾效果增進率分別為49.1%與 51.4%，而100W鎢絲燈強制對流方面過濾效果增進率則為60.2%。由整個研究結果可以發現，本燈具對於空氣清淨有極佳的效果，在不增加額外耗能條件之下，能增加燈具的散熱效果與延長壽命，同時又具備空氣清淨效果，對環境空氣品質具有相當的貢獻。 The purpose of this study is to develop a novel lamp with both the functions of air-cleaning and lighting. One of it is the desk light. Basing on free convection principle, it makes the air run through the filter on the top of the lamp by its heat in order to attain the aim of air cleaning. To find the optimum value of both cleaning effect and illumination, we advanced the compare factor. The other is the droplight, though it is based on the same principle, we use the solar energy as its power to drive the fan. So that the effect of the filter can be augmented and the result of this research approach perfect. According to the experimental result, in the four-week experiment with desk light, the enhanced efficiency of filter is 39.1%, 40.8% and 40.1% respectively. On the way of droplight with four-week experiment, the enhanced efficiency of filter is 49.1% and 51.4% with helix and tungsten(100W) lamp under the condition of free convection; the enhanced efficiency of filter is 60.2% with tungsten(100W) lamp under forced convection. All these results of the research shows that the novel lamp has great performance on air cleaning and much better effect of heat sink without extra consuming of energy, also the lifespan of the lamp can be extended. Furthermore, it is capable of air cleaning and contributes to the quality of environmental air.

目前正逢能源危機之際，能源再生成為全球關注的課題。有鑒於此，本研究應用高導磁環形鐵粉芯，在表面纏繞多圈漆包線，形成環形管(Toroid)。環形管外圍再繞上交流電源線，電源線內電流產生的磁場，被高導磁環形鐵粉芯所引導，產生較強而均勻的磁場，傳遞至內圈的單心漆包線環形管，依法拉第定律產生電動勢，達到能源再生的目的。藉由六項實驗，驗明我們研究雙環形管理論，推演所得的電動勢公式 ε＝(μN1N2/2 r) a2ωIo cosωt 是正確的。再生的電動勢能驅動高亮度的發光二極體提供照明、電器產品充電；還能提供電流過載警示，防止電路過載起火的危險；串、並聯使用則可產出較大功率，深具應用與研究的價值。During mankind are urgent developing of new energy, recycle energy are also one of the global topics; we are using single-heart-Turn around how the high permeability enameled wire ring formation of iron powder core ring solenoid, from the external power supply line also used around - Ring solenoid (Toroid), due to changes current power supply lines of magnetic field generated by the high-permeability core Ring guided iron powder, and can produce more uniform magnetic field so that the inner ring of single-heart enameled wire Ring solenoid, according to Faraday's Law electromotive force can be generated to achieve purpose of recycle energy, we will be divided into six experimental studies to confirm this theory deductions obtained by electromotive forceε＝(μN1N2/2 r) a2ωIo cosωt is correct, this electromotive force will enable to supply high brightness LED Optical lighting, can also be used for current overload warning system , if use on series-parallel connection that will produce larger power output, it has great application potential, so the subject is worth to research and development.

To-be static objects, such as bridges, volcanoes, seldom move ordinarily but have mini displacement only under special conditions, like flood or earthquakes. Therefore, how to measure their mini displacement has never become fully popular with scientists’ research. Then, beginning with “ Optical Lever Theorem”, through a series of speculation and discussion, I decide to use laser ray as light source to perform an experiment ------- trying to find objects with mini displacement in our daily lives, such as revolving electric fans, engine-opening motorcycles, shaken trees, testing their magnifying effect first. Next, I try to use the control-experiment method to find out the magnifying relation and formula of the rotation angle of the plane mirror and the displacement quantity of light focus. As to the measure of mini displacement on objects, I utilize the pillar mirror as a reflection plane to research the magnifying relation of reflection light focus and original displacement quantity. The image made from the light focus of pillar mirror’s reflection, however, isn’t so perfect that I have to use a special plastic-made light-concentrating mirror, which is also called “ Fresnel Lens ”, to focalize the light for easy observation. Besides, I find out the “ function graph ” of the mini displacement quantity on to-be static objects and the displacement quantity of reflection light focus. At last, I try to build up a “ Bridge Alarm System ” of Optical Lever Theorem. 準靜物如橋樑、火山，由於平常不輕易移動，只有在特殊情況下（如洪水、地震）時，才會發生位移的現象。因此，其微小變位如何測量，一向是科學界較少探討的題目。於是，先由光學槓桿原理著手，經過一番思考、探討，決定採用雷射光作為光源，並作了第一個實驗－－找生活中具極微小變位的東西，如轉動中的電扇、引擎發動的摩托車、被搖動的樹木等，先測試其放大效果。接著就試圖用控制變因的方法，找出平面鏡旋轉角度和光點平移量的放大關係和公式。至於物體微小的平移量之測量，則是利用柱面鏡作為反射面，來探討反射光點的位移與本來的平移量之放大關係。然而，柱面鏡的反射光點成像並不理想，於是用一種特製的塑膠集光鏡，又稱Fresnel Lens，將光點集中以利觀測，並且找出準靜物之微小平移量及反射光點的位移量的函數圖形。最後，嘗試建立一套光學槓桿式的「橋樑預警系統」。

Quantum Rings are defined to be polygons with sides all of the same unit length that are connected with a fixed positive or negative angle. In the research, the number of Quantum Rings corresponding to a given number of sides and a fixed angle will be discussed. Quantum Rings could be expressed by many sequences which would involve the theory of partitions and ways to eliminate the many to one nature of the sequences in order to evaluate the upper and lower bound. Besides estimating the upper and lower bound, a lot of the qualities of the Quantum Rings under certain circumstances will be mentioned.「能量環」為許多單位長度的線段以定角首尾相接，並且最後接回原點的多邊形。本研究將要探討對於給定邊長個數與相接角度的「能量環」的個數。「能量環」可以被表示成許多種數列的形式。在數列的運算中會牽涉到許多數字分割的理論與排列組合的排除重複以求得能量環個數的上下界。除了定量的求算出上下界以外，報告中也定性的歸納出許多給予特殊條件的能量環的性質。

本研究主要探討蝌蚪之游泳運動特性，及游泳速度(V)與尾鰭長度(SL)、尾鰭高度(SH)、身體質量(M)、尾鰭擺動頻率(TBF)、擺動幅度(AMP)之關係，並分析蝌蚪游泳之體軸變化及流場變化。祈能了解蝌蚪之游泳運動特性，進而探討其適應環境之機制。研究結果顯示：黑眶蟾蜍蝌蚪體重(M)愈重，則鰭長、鰭高亦隨之生長，並呈現高度相關性(R2=0.9381、R2=0.9809)。另外，尾鰭生長時之長度增加較多。蝌蚪體重(M)與鰭長(SL)、鰭高(SH)之迴歸方程式(M=0.027SL＋0.342SH－0.078，R2＝0.9832)。黑眶蟾蜍蝌蚪之游泳速度，會隨著尾鰭擺動頻率之增加而提高。尾鰭長度愈短之蝌蚪，增加游泳速度時尾鰭擺動頻率增加較多。蝌蚪游泳速度(V)與鰭長(SL)、擺動頻率(TBF)之迴歸方程式(V=0.480TBF＋4.804SL－4.381，R2＝0.9110)。不同尾鰭長度蝌蚪之擺幅對體長之比率並無明顯變化，其擺動幅度(AMP)的範圍介於0.45(BL)至0.56(BL)之間。蝌蚪游泳時各部分體軸之擺動幅度自吻端開始(P=0)至P 為0.24 時逐漸遞減，且在P 為0.24 時呈現最小擺幅，但P 超過0.24 之後直至尾鰭部分卻又大幅遞增，其最大值出現在尾鰭末端(P=1)。蝌蚪游泳是以尾鰭快速向中心軸擺動，產生較大的前進動力，過了軸線則慢速擺動，以減少阻力。This investigation is to explore the swimming habits of tadpoles- the relationship between their swimming velocity, length and height of their tails, mass, the frequency at which their tails movement, and the amplitude of the tail’s movement, as well as analysis their body axes, and the flow distribution of the water, in order to understand how the swimming patterns of the tadpoles are affected by the changes in their environment. The results of this investigation have shown that as the mass of the tadpoles increases, both the length and the height of their tails also increase according to the R values of the tail increases according to the R values of 0.9381 and 0.9809. However, it is observed the length of the tail increases at a faster rate than its height during the tadpoles’s growth. The formula which models the regression relationship between the tadpole’s mass, tail length, and tail height are found to be (M=0.027SL+0.342SH-0.078,R=0.9832). It’s also noted that as the length of the tadpole’s tail decreases, the velocity and the frequency of the tail would increases (the length of the tail is inversely proportional to the tadpole’s velocity and tail frequency). The formula which models the regression relationship between the tadpole’s velocity, tail length and tail frequency is (V=0.480TBF+4.804SL-4.381,R=0.9110) The different frequency model by tails of different lengths do not appear to have an apparent relationship with the tail length, given that the amplitude is between 0.45(BL) and 0.56(BL). As the tadpole swims, the angle between its oscillating body axes decrease as the P values increases from 0 to 0.24, their force the angle is at a minimum whom the P is at 0.24.Yet when P exceeds 0.24 the angle would increase dramatically. The maximum value is observed when P=1.The tadpole’s swimming motion mainly relays on the rapid oscillations of the tail about the centre of mass (body axis)-producing a stronger driving force, and slowing down towards the end of each oscillation to minimise the friction forces acting on the tadpole, which in furn, decrease its velocity.