我們從市售的果凍凝膠冷/熱敷袋得到靈感，一般冰凍包只能使用一次，內容物呈液態，在延伸研究中，我們以「尿素冰包」為基礎，設計「複合凝膠態環保冰包」，使它更具有應用的價值。： 1. 自製環保冰包，可降溫達15.2℃，最低溫度可達7.8℃，體感溫度約5℃，保冷時間可以達到40分鐘(≦15℃以下)。 2. 我們發現最有趣的應用是置放於過熱的手機或平板後方降溫，實測可在5分鐘內使過熱手機降溫10〜15度。 3. 使用過後的冰包，可以冰凍後，再放入冰桶或者是攜帶式保溫袋中當成「保冷劑」使用。 4. 使用過後的環保冰包，可加水稀釋100倍，當作肥料澆灌植物，約兩周後即可以促進植物葉子的生長。 5. 自製環保冰包成本低廉，小型環保冰包製成一包成本只要4.35元。

(一)爰對於蘭陽地區採集蝶類已有三十年之久，對於本省各地區蝶類之分佈，雖已獲致初步概念，但是「生態’及「食草」問題仍是撲朔迷離，因此針對這方面做進一步之研究，期能有所瞭解。(二)幼蟲發現經過： 1966 年 8 月 20 日在海拔1850公尺的太平山（獨立山）採集蝶類標本時，無意中在 r 臺灣擦樹」 sussafras Randaiense 葉之表面上發現深綠色不規則斑紋的終齡幼蟲，即將牠及樹葉帶回家飼養至 8 月 23日變為前蛹，過冬至翌年， 1967 年 5 月 6 口竟意料不到的寬尾鳳蝶（♀）羽化。過冬蛹期為八個半月，共 255 天之久。為了幼生期之生態及其他有關疑問甚多，未能一一瞭解，囚此自 1966 年至今約十八年斷斷續續跑遍了山野、河谷，在這十幾年當中，所搜集有關問題、卵、幼蟲、成蟲，其生態、習性、生長環境，及其他有關問題獲得了了解。

衛生紙看似簡單，內容卻不簡單，我們發現平版式衛生紙與抽取式衛生紙的花紋類型、張力、吸水性和承載重量都不相同。我們以實作方式統計小朋友適當手掌長/寬度的測量，分析一元所能購買的衛生紙數量，透過訪問方式進行購買動機的行為調查，讓我們發現生活必需品-衛生紙，充滿了有趣的學問。希望大家檢視自己的行為習慣，為節能減碳盡一份心力。

蝙蝠俠跟蝙蝠最大的不同在於：前者是依靠視覺感應來活動的人類，而後者是利用聽覺來感測周遭環境的夜行性動物，不能因為兩者名字相近就當作是相同的東西。蝙蝠在飛行時，能利用其喉部肌肉的收縮來製造超音波，再經由嘴或鼻子發射出去探測四周的環境，當周圍有障礙物時，它能藉由超音波撞擊到物體反射的回波來了解周遭的情形。蝙蝠的超音波頻率依種類不同而多變，而且其具有極佳的回聲定位(echolocation)能力，這種能力除了能讓蝙蝠清楚定位出餌（大部分是昆蟲）的距離、方向和形狀，更能知道障礙物和自己本身的位置所在。當然蝙蝠不僅在飛行時會發出高頻率的超音波，更會在受到干擾或與同伴間聯繫時發出聲音，前者稱之為定位聲，後者稱為聯繫聲，其頻率較低，人類通常可以聽到。 作者：陳怡安 審查：林明聖

本文我們研究下列問題： 1. 何時心律會成穩定的狀態呢？ 2. 是否能建立出心律穩定的數學模型？ 3. 什麼樣的函數會使得心律趨於穩定？我們以xmp+i 表示第p+1 個訊息傳到第i 個細胞之前，第i 個細胞的舒張時間，而且xk 和 xk−m, xk−m+1,..., xk−1的關係為 In this paper we study the problems as follows: When will the rhythm of heart beats approach to a steady state? Can we set up the mathematics model with steady rhythm of heart beats? What kind of function will make the rhythm of the heart beating tend to be stable? The result of our study is as follows:

池塘內、溪河裹、海洋中有萬千的魚類，每種魚都有牠漂亮的外衣，五花十色，不僅如此，牠們還會代代相傳，子子孫孫都有類似的色彩，這些美麗的色彩是不變的，此種呈色乃生物色素 (B- iochromes ）的結果；但有些魚類為了保護自己，靠改變自己的體色，以配合外界環境，來掩飾自己，逃避敵人，就達到如同昆蟲的保護色作用，像比目魚(Flounder)體色的改變。而這種體色的變化，必定是由特殊色素系統所發生的，絕非像不會變化的生物色素，而且它一定有特別的控制機構，色素細胞(Chromotophore) 常存於魚的皮膚上，也就是前述所謂的「特殊色素系統」此種細胞台因外界環境改變，而改變其呈色方式。許多關於色素細胞的間題，必須靠仔細的觀察及實驗才能解決，於是我們利用常存於鯽魚、金魚皮膚的黑素胞(MelanoPhore) 來做實驗，以求探討一些有關色素細胞的問題。

傳統的畢氏定理三元二次不定方程x² + y² = z²有一組漂亮的整數解為(m² - n²、2mn、m² + n² )；中國數學家嚴鎮軍、盛立人所著的從勾股定理談起一書中記載四元二次不定方程x² + y² + z² = w²的整數解為(mn、m² + mn、mn + n²、m²+ mn + n² )，這組解被我們發現有多處遺漏，本文以擴展的畢氏定理做基礎修正了他的整數解公式，並推廣取得N 元二次不定方程的整數解公式。 There is a beautiful integer solution formula for the Pythagorean theorem equation, x² + y² = z² , such as (m² - n² , 2mn ,m² + n² ). The “m＂ and “n＂ of the solution formula are integer number. A book written by two Chinese mathematicians, Yen Chen-chun and Sheng Li-jen who expanded the Pythagorean theorem equation to the four variables squares’ indeterminate equation, x² + y² + z² = w² . They claimed that they found its integer solution formula, such as (mn , m² + mn , mn + n² , m² + mn + n² ) for any integer “m＂ and “n＂. But we found it losses many solutions. This paper corrected their faults due to the expanded Pythagorean theorem built by ourselves. Further more, we derived a general formula of N variables squares’ indeterminate equation. Now, we can get integer solutions of the equation, (for all natural number “n＂) easily by choosing integers m1 , m2 , m3 ,……, mn−1 up to you.

The aim of the work is inventing the way in which the power of the ICE is the same and consuming of the fuel decreases. The following methods of investigation were used: analysis of the experience of the improvement of ICE, modeling, the brainstorming, methods of Decition Theory of Invention’s Tasks (DTIT). In this work Ivan Semyonov based on a hypothesis that if the non-supporting combustion exhausts will be drawn with the vacuum from cylinder fuel for the same power it needed less. The practical meaning of this work is in the attempt of studying the question of improving the ICE for getting and making the more perfect ICE.

令Sn 為{1,2,…,n}任意排列所成的集合，π ? Sn 為其中的一個元素，我們記π = (π(1), π(2),…, π(n))。今給定π ? Sn ，若對所有i,1? i ? n，都有π (π (i)) = i 時，我們稱π 為involution。假設π ? Sn ，並給定σ ? Sm (m ? n)，當π 中任取m 項，其大小關係的順序都和σ 不同，我們稱π 避開σ，或稱π 是一個σ-avoiding 排列。在這篇報告中，我們主要分析了2143-avoiding involution，1234-avoiding involution，和3412-avoiding involution 中的一些統計量，給出了十數個結果與幾個猜想。Let Sn be the set of permutations on {1,2,…,n} and π ? Sn be an element in Sn. Denote π as π = (π(1), π(2),…, π(n)). We say that π is an involution if π(π(i)) = i for every i, 1? i ? n. Given π ? Sn and σ ? Sm (m ? n) , we say that π avoids σ (or π is an σ-avoiding permutation) if π does not contain any m-term subsequence in the order of σ. In this paper, we discuss some classic statistics on 2143-avoiding involutions, 1234-avoiding involutions and 3412-avoiding involutions. We get many new results in this field and give some interesting conjectures.

The Red Palm Weevil is a kind of pest commonly found in all coconut and palm growing areas, causing considerable damage to palm trees. The pest at larva stage was found to be a popular food dish for both local people and visitors and has been commercially bred for consumption. This project aimed to develop a farming method to increase the quantity of red palm weevil larvae for commercial use, instead of the natural farming which fed the insects on rare natural materials. Firstly, the most appropriate food formula to boost the multiplication of red palm weevil using local raw materials was determined. Four food formula were developed: 1.combination of palm leaves, coconut fibers, and pig food, 2.palm leaves, coconut fibers, and rice bran,3. palm leaves, coconut fibers and cassava,4. a combination of crushed palm leaves and coconut fibers. The mixture ration were 1:1:1 for formula1-3 and 1:1 for formula 4. Equal number of the adult weevils were raised in the different food formula, the length and weight of the larvae obtained were measured every week for seven weeks. The gross weights and the effectiveness of the red palm weevil farming were analyzed using the feed conversion ratio (fcr), the daily growth rate, and the percentage increase in weight. It was found that. the weevils raised with food formula 1 yielded the larvae which grew the fastest with highest effectiveness. The most appropriate ratio of the food mix which yielded the satisfactory larvae size was determined to be 1:1:1 3.Next, experiment was carried out to improve the quality of the insect larvae for consumption. The larvae produced had some distinct smell which some consumers do not like.To improve the smell, the larvae were fed with the selected food mix added with minced fresh Pandanus leaves 2 days prior to consumption. Food mix with coconut fibers instead of Pandanus were used as control. Consumers were most satisfied with the larvae fed with added Pandanus leaves. Analysis of the food mix, larvae and Pandanus leaves found the common compound, Coumarins. In conclusion, our project found a suitable system of red palm weevil farming an alternative to conventional method which farmed the pest on cut palm trees. The new method resulted in the best yield of insect larvae with the highest consumer satisfaction and reduce destroying natural resource.