臺灣

Sicherman 已經找出與兩顆六面的正常骰子有相同機率分布的Sicherman 骰子，並進一步獲得與三顆六面的正常骰子有相同機率分布的骰子必為一對Sicherman 骰子與一顆六面的正常骰子之結果，我們試圖由已知的Sicherman 六面骰子的處理方法出發，透過對割圓多項式的分析來累積足夠的相關資料，以處理由兩顆四面骰子至兩顆三十面骰子，處理由三顆四面骰子至三顆三十面骰子的各種Sicherman 骰子的答案，來探索兩顆與三顆的n 面Sicherman骰子存在的充要條件與求法，並進一步將所得之結果分類，得到 ”有相同標準分解式的類型的數n，會具有相同組數的Sicherman 骰子”之猜測結果與特殊情形下的證明。 Sicherman has found out the Sicherman dice which have the same probability distribution as the normal two six-sides dice. Furthermore , he also found out a pair of Sicherman dice and a normal six-sides dice has the same result as 3 normal six-sides dice . We try to begin with the given algorithm of six-sides Sicherman dice , through the analysis of Cyclotomic Polynomials to accumulate sufficient related information then to come up with the solution from discussion of 2 four-sides dice to 2 thirty-sides dice , from 3 four-sides dice to 3 thirty-sides dice to explore the existence of necessary and sufficient condition and solution of 2 n-sides Sicherman dice and 3- sides Sicherman dice , and even to classify the results to come to a conclusion of the guessing results and proofs under special cases about “the numbers n which have the same Canonical Prime Factorization will have the same numbers of n-sides Sicherman dice.”

脊髓性肌內萎縮症為常見之體染色體隱性遺傳性疾病，在台灣罹病率約為萬分之一，罹病者會造成幼兒期致死或因肌肉萎縮導致殘障。大多罹病者致病成因為SMN基因突變，脊髓前角運動神經元凋亡退化，導致上下肢肌肉發生漸進性萎縮

本研究以攝影紀錄的方式，透過電腦進行影像分析，記錄不同刺激下美洲蜚蠊(Periplaneta americana)的觸角擺動模式，計算出各項觸角運動的參數，以瞭解光線(光刺激或光適應)、震動刺激、喝水與進食對其觸角行為的影響。我們發現在不同因子的刺激下，觸角擺動的模式具有差異，若兩種不同的刺激同時發生，蜚蠊觸角的行為亦具整合性的反應。蜚蠊於不同狀態下(如喝水或進食)，對相同的刺激有不同的反應，證明蜚蠊觸角的行為模式，受環境因子與個體狀態調節。透過掃瞄式電子顯微鏡的觀察，也發現觸角具多種感覺毛，且雌雄的感覺毛的分佈與數量具有差異。綜合以上發現，證明觸角除了為敏感的受器，亦為能反映出生理與環境狀態的動器，同時也適合進行發展檢測器的仿生學應用，用來檢測環境中物理及化學因子。The aim of this study is to investigate the different swing motion modes of antennae of American cockroach (Periplaneta americana) by computer-aided Imaging Analysis. The parameters of each swing movement were calculated in order to analyze how light (including light stimulation or light adaptation), vibration, food and drinking water may affect the antennae behavior of American cockroach. It was found that the antennae swing motion modes were significantly different under different types of stimulus. If two different types of stimulus occurred at the same time, the reactions of antennae motion may become conformable. Under different environmental conditions (such as food or water), same stimulus may result in different reactions. The antennae behavior has shown to be significantly affected by environmental conditions and individual physiological status. Through the observation with scanning electron microscope (SEM), it was found that the antennae has many types of sensilla; and the distribution and quantity of these sensilla are significant different between sexes. In conclusion, not only the antennae are considered as the sensitive receptors, but also they are the important effectors to reflect physiological status and environmental conditions. The current model is suitable for the development of specific detectors in the applications of Bionics to detect the physical and chemical factors in certain environments.

This experiment mainly aims at three kinds of solution - Dextrose, Saccharose, and Fructose. By changing its temperature, density, length of tube, as well as different wave length factor of polarized light, we observe the influence of the direction of polarization by those factors. The experimental result showed as follow. The Dextrose and the Saccharose can cause the polarized light with the rotary direction of clockwise, so both are ‘dextrorotatory’. The Fructose can cause the polarized light with the direction of counterclockwise, so it is the ‘laevorotatory’. For the Dextrose, when the\r temperature is lower than 20℃, the direction of polarization has changed observably, but doesn’t have any rule. When the temperature is higher than 20℃, the direction of polarization increase slowly. For those three kinds of solution, when\r density increased, the polarization increased observably. When the polarized light passed through the solution with longer path, the direction of polarization has more change. When the wave length of the polarized light changed, the direction of polarization has been changed observably. When the wave length of the polarized light is shorter, the direction of polarization change increased.本實驗主要針對葡萄糖、蔗糖、及果糖等三種旋光性溶液，改變其溫度、濃度、容器管長、以及不同波長的偏振光等因子，觀察這些因素對偏振方向所造成的影響。實驗結果顯示：葡萄糖與蔗糖會使得偏振光的偏振方向以順時針旋轉，屬右旋性之光學異構物；果糖會使得偏振光的偏振方向以逆時針旋轉，屬左旋性之光學異構物。若溶液為葡萄糖，當溫度低於20℃時，偏振光的偏振方向會有明顯的改變，但無規則可尋；當溫度大於20℃時，偏振方向旋轉角位移則以非常緩慢的方式增加。當此三種溶液之濃度增加時，偏振光的偏振方向有明顯遞增的現象。此外，當容器長度越長（即偏振光在介質中的行程越長）時，偏振方向的改變亦越明顯。當偏振光的波長改變時，偏振光的偏振方向有明顯的變化，且當偏振光的波長越短，偏振方向的改變越大，似乎與波長呈反比，但此結果與理論值（即旋光度與波長平方成反比）仍有一些差距。

動脈硬化是個致病率和致死率相當高的慢性發炎疾病。HMG-CoA 還原酵素抑制劑 纇藥物，簡稱statin, 是一類強效的降血脂藥物，而且在臨床上對於心血管疾病有廣泛的 治療效果。然而近年來的研究報導指出，statin 會有如此廣效治療效果，其原因不僅僅 是因為它的降血脂能力，而是statin 也具有抑制發炎作用的效果。雖然臨床上已經證實 statin 可以減緩動脈硬化的病程，但是statin 對於誘發型一氧化氮合成酵素(iNOS)表現的 調控機制還不明確。有文獻指出NOS 代謝產物nitric oxide (NO)可以改善血流，而可能 在動脈硬化上扮演保護角色。值得一提的是雖然適量 NO 有維持血管恆定的功能，過 量時則會造成血壓過低休克的現象，這就是細菌感染後因內毒素 lipopolysaccharide (LPS) 作用引發敗血性休克的主要原因之一。在本實驗中，我們使用fluvastatin、lovastatin、 pravastatin 和 atorvastatin 這四種statins 來探討它們對於血管平滑肌細胞由LPS 及IL-1β 誘導iNOS 基因表現的影響。我們發現，statin 可以抑制LPS 所誘發的NO 和iNOS 表現， 但卻會促進IL-1β所誘發的反應。NF-κB 在iNOS 的基因調控上扮演重要的角色，而在 探討NF-κB 被LPS 和IL-1β活化的情形中，statin 同樣會促進IL-1β活化NF-κB，但抑制 LPS 活化NF-κB。我們也發現fluvastatin 對於IL-1β所引發NO 的產生、iNOS 的表現、 NF-κB 的活化，以及p65 向細胞核移動的促進作用，在ROCK 抑制劑Y-27632 的處理後 可以看到相同的現象。IKK kinase assay 顯示Y-27632 對於LPS 所促進的IKK 活性影響 很小，但是會促進IL-1β的活化作用。接著，在ROCK 的活性方面，LPS 會抑制原本已 表現的ROCK 活性， 而相反的，IL-1β會增加ROCK 的活性。總括來說，這些結果顯示 ROCK 在血管平滑肌細胞中扮演IKK/NF-κB 的負向訊息調控者角色，而這個機制在LPS 和IL-1β的訊息傳遞路徑中有不同的調控。即ROCK 以負向調控機制角色影響IL-1β的 訊息傳遞，卻不存在於LPS 的情況中。就是因為透過反轉這個負向調控的機制，statins 3 和ROCK 抑制劑對於LPS 及IL-1β引發血管平滑肌細胞的iNOS 表現，呈現相反的調控 結果。這些作用可能參與statin 預防血管再阻塞，抗發炎，抗動脈硬化的作用。此外Statin 抑制LPS 的iNOS 表現作用或許將來可運用於治療敗血性休克。利用基因微陣列分析也 偵測到一些受fluvastatin 正向或負向調控的基因，目前我們正朝鑑定基因的表現改變及 確認其功能，生理意義進行實驗中。 The 3-hydroxy-3-methylglutaryl (HMG)-CoA reductase inhibitors, statins, are potent inhibitors of cholesterol synthesis and have wide therapeutic use in cardiovascular diseases. Recent evidence, however, suggests that the beneficial effects of statins may extend beyond their action on serum cholesterol levels. Although statins have been shown to reduce progression of atherosclerosis, little is known about mechanism by which statins affect iNOS expression. Optimal level of NOS product, NO, possesses the anti-inflammation and anti-proliferation effects in atherosclerosis, while large amount of NO contributes to the septic shock in response to bacterial endotoxin, lipopolysaccharide (LPS). In this study, we investigated the effects of fluvastatin, lovastatin, pravastatin and atorvastatin on IL-1β- and LPS-induced NO production in cultured rat vascular smooth muscle cells (VSMC). We found statins can inhibit LPS-induced iNOS expression and NO production, while they can potentiate IL-1β-elicited responses. In studying the activity of NF-κB, which plays an important role for iNOS gene induction, we found that fluvastatin can increase IL-1β-induced p65 nuclear translocation and NF-κB activity, while inhibit those induced by LPS. The potentiation effects of fluvastatin on IL-1β-induced NO production, iNOS expression, NF-κB activation and p65 nuclear translocation were all mimicked by a ROCK inhibitor, Y-27632. IKK kinase assay showed that Y-27632 itself has minimal effect on LPS-induced IKK activation, while enhances the response of IL-1β. Studies on examining ROCK activity showed LPS can downregulate constitutive ROCK activity, while IL-1β oppositely increases ROCK activity. Taken together these data suggest ROCK is a crucial negative regulator of IKK/NF-κB signaling pathway in VSMC, and this negative control is existing in the action IL-1β, but is absent in the action of LPS. Through abrogating the function of this negative regulator, statins and ROCK inhibitor thus differentially regulate iNOS expression induced by LPS and IL-1β in VSMC. These results suggest that stimulation of iNOS expression in the presence of IL-1β might contribute to the beneficial effects of statins in atherosclerotic process in terms of vasodilation, anti-inflammation and inhibition of smooth muscle cell proliferation. In contrast, the diminishing effect on LPS-induced NO response possibly may provide new therapeutic strategy in sepsis. Al these results strengthen the pleiotropic actions of statins in anti-inflammation and anti-atherosclerosis. Preliminary microarray analysis further revealed several genes either upregulated or downregulated by fluvastatin. The identification of these genes and studying their functional roles in atherosclerosis are currently in progress.

人體表面積在醫學的應用相當重要：燒燙傷的評估是以全身面積被灼傷的百分比 表示；營養狀況的評估，新陳代謝率也以單位表面積表示之；體液或藥物之需求量也 是以體表面積來決定劑量；然而人體是一不規則物體，應用一般幾何面積計算公式有 其困難處，如何快速的計算人體表面積，以作為醫療的指引，有其必要性。而青少年 正處於快速發育期，各部位的成長是否會影響表面積的計算，由於目前鮮少對青少年 之專文報告，尤其缺乏台灣地區之調查。為了探索這些問題，乃進行調查與研究。 本研究以台灣地區國民中小學10 至15 歲青少年為對象，探討在此發育期間體格 之變化及可能之影響相關因子，並建立體表面積之快速計算公式。本研究隨機取樣以 1209 人形成樣本，其中男生623 人，女生586 人，利用尺秤，取得身體各部位的資料， 並以問卷調查運動、飲食與睡眠等問題，以探討影響此成長期發育之因子。結果發現： 台灣青少年體表面積快速計算公式為(身高x 體重 ÷37)0.5；其體表面積九分法計算方 式也有別於一般歐美成年人的計算法；及此年齡層的身高與體重受運動的頻率、運動 持久性、飲食習慣多寡的影響，而與運動種類及主食種類相關性不大，這項研究的發 現，將有助於醫護人員對青少年問題的處理。Body Surface Area (BSA) has been used in many clinical conditions to calculate the percentage of burned area, to evaluate the nutrition status - the unit of the metabolic rate, to determine the need of fluid supply or the medicine dosage requirement. So precise measurement of BSA is very important, however the human body is an irregular shape, a laborious task using the geometrical method. To establish a simple quick formula to guide the therapeutic treatment is a necessity. Also the rapid growth phase during the adolescent stage might change the BSA in some way. BSA has not been established for the teenagers in Taiwan. To investigate this issue, a total of 1209 healthy elementary and junior high school boys (623) and girls (586) aged 10 to 15 in Taiwan were recruited by random selection. By use of anthropometrical measurements and a health questionnaire to the subject simultaneously, the data was analyzed statistically. The results revealed that a quick adequate formula derived from the body height and weight for Taiwan teenagers was determined by the formula, BSA = [ Height (meter ) x Weight (Kg) ÷37 ] 0.5, the Taiwan teenage “rule of the nine” of BSA is different from that of the adult, and that the frequency and the duration of exercise, the diet habit, and the duration of sleep significantly influence both body growth and weight. These findings may provide significant references for the physicians to treat the clinical conditions of teenagers in Taiwan.

在這篇報告中，我們探索了「將錯就錯的Knuth 河內塔問題」。傳統河內塔問題在電腦科學上佔有重要的地位，是一個極具內涵的模型。由於這個模型的深厚數學內涵，使其和巴斯卡三角形建立了緊密的連結，且利用這個緊密的數學連結，設計出復原任意起始狀態的良好演算法。Knuth 河內塔起因於數學家Knuth 在論文[3]中，描述傳統的河內塔問題時所發生的一次筆誤。在這個新的規則之下，我們意外發現Knuth 河內塔存在著一個和傳統河內塔平行的模型，此模型在電腦科學及數學上有著完全不同於傳統河內塔的內涵。我們的研究主要如下：(分別為內文中的四大段)(一) 結構分析。移動環所需要的次數，如何移動環並分析每一次動作所動的環，及每個環何時被動到並給出演算法。(二) 正整數的分割。所有的移動步驟將正整數做了一個新的分割(Partition)；此分割模k之後有良好的循環性質。(三) 費波那契真分數的排序。這個正整數的分割形成一張表，這張表恰好就是分子分母皆為費波那契真分數之排序。(四) 隨意亂排的Knuth 河內塔復原演算法。在Knuth 河內塔的規定下將起始狀態改變，找出良好的復原演算法，並分析。 In this project we study the "Knuth Hanoi Tower", which is motivated by a typo in a paper of Knuth. This inadvertently typo leads to a new rule of moving the discs on the Hanoi Tower (see introduction below for definition). Although seemingly similar to the traditional Hanoi-Tower problem, it turns out that under this rule the "Knuth Hanoi Tower" problem consists of amazing properties, and is totally different from the traditional one. Our study focuses on the following directions: (1) Structure analyzing: We analysis the sequences recording the disc moving and offer enumeration results and recurrsive/non-recurrsive algorithms. (2) Partition of N: The moving sequence forms a partition (a table) of N, which has an amazing congruence property. (3) The order of Fibonacci proper fraction: The row/column of the partition table is, even more amazing, exactly the order when sorting the Fibonacci proper fraction with fixed denominator/numerator. (4) The Restoration of an arbitrary initial state: We offer an efficient algorithm for restoring any initial state of discs. We hope that our study on the "Knuth Hanoi Tower" offers a simple, neat, and new example on the theory of Algorithm, Number theory and Combinatorics.

最後留下數字會是多少？該問題在台灣的全國中小學科學展覽出現多次。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，不論是歷屆全國中小學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。本研究利用獨創α分類、n 及k 分類、d 函數、b 函數及循環、n 及y 分類、碎形數列和演變關係，將約瑟夫問題探討範圍提升至殺α(個數)留β(個數)，直到剩下最後1 個數時就不能再殺了，遊戲終止，倒數第k 個留下的自然數是多少？同時，本研究在殺α(個數)留β(個數)下，指定自然數y 為酋長，酋長不能被殺，殺到酋長時遊戲停止，求剩下的自然數有幾個？會發生什麼情形？The Josephus problem refers to what will be remaining when arranging n natural numbers in a circle and starting killing one and leaving the next one alive. The problem has been on display for many times in Taiwan National Primary and High School Science Exhibitions (as shown in Table 1). And, the information algorithm master, Donald E. Knuth has elaborated on the array in his works The Art of Programming, CONCRETE MATHEMATICS. However, both the past science exhibitions and the master’s works are limited to discussions on cases of killing 1 leaving β or killing α and leaving 1. This research employs uniquely created α classification, n and k classifications, d function, b function and loop theory to extend the Josephus problem scope to killing α leaving β to find out what the remaining natural number is by No. k counted recursively. Meanwhile, this research designates natural number y as the chieftain, which can never be killed. The game is over when the chieftain is to be killed. The problem is to work out how many natural numbers are remaining. And what happened?

二氧化鈦是光觸媒中最常被使用的，雖然合成方法很多，但如何提升其產量及分解效果，一直是學界及業界的熱門議題。\r 在此篇報告中，我們發展出一種新的方法來製造二氧化鈦，利用控制合成時溶液的pH值、使用幾丁質當作新的保護劑，並且改變加熱的溫度和時間來得到二氧化鈦奈米顆粒。在降解實驗中亞甲藍光的分解反應速率級數為一級，降解亞甲藍液的半生期在2.9~7.0分鐘，比一般文獻的數十分至數小時以上的速度高出許多。\r 另外，在幾丁質未燒去的實驗中，我們發現亞甲籃分子會被吸附在幾丁質的表面上但不被分解，燒去幾丁質時奈米粒子又無法完全分散，為解決這一個問題，我們使用了分子篩，分子篩可以吸附許多有機物質，再加上其為具有許多中/微孔構造的鋁矽酸鹽礦物，奈米粒子可以分散在其表面而不生團聚；在光降解的實驗中發現光觸媒結合分子篩後可大幅提高染料的分解效果，在短短一分鐘之內便將亞甲藍分解掉一半以上！\r 這個實驗提供了很好的方法，可以快速有效的合成二氧化鈦奈米顆粒，作為光觸媒使用。我們相信這個方法可以推廣到其他有機汙染物質，以降低工業進步後對地球環境所造成之污染危害。

The spiders, Neoscona nautica, often appear in groups, but individuals have their own sense of territory.They usually spin webs among branches during 6:00~ 8:00 in the evening. When building webs, they will first start with bridges and then spin Y-shaped spokes. Next, they spin meshe of net, silk frame, spokes, spirals and free-zone in order. After finishing webs, they will wait for prey on the free-zone or meshe of net. If they find something inanimate on the web, they will break the spiral attached with the inanimate object that is later removed. If the meshe of net is broken, they will fix it immediately. For them, the time to take webs back is during 2:30~ 6:00 in the morning. Most time they use the first pair and the second pair of legs to take webs back and swallow the webs. Sometimes, they break the spirals by the last pair of legs. The sequence to take webs back is : lower right section, lower middle section, lower left section, upper left section, and upper right section. At last, one thread of bridge will be left. Every early mornings they take webs back and swallow them. The next evening they rebuild webs. Possibly there are two reasons to explain why spiders eat their webs: (1).They swallow webs to get protein. (2).The web threads are easily polluted by dust and humidity and reduce stickiness. The web may also reduce the probability of capturing prey. The body length of them is not related to effective web dimensions. However, the web sizes depend on the width of web-building location. The study shows linear relation among body length, meshe of net and dimensions of free-zone. The linear relation represents that the meshe of net and free-zone have ecological or survival meaning for them. We expect that this study of Neoscona nautica can be helpful to build spider ecological database in Taiwan.簷下姬鬼蛛常成群出現，但個體卻有很強的領域性；常於下午6：00 至8：00 結網於樹枝間，結網時，先以橋絲為出發，織出一Y 形的縱絲，再由此依序織出中空網眼、絲框、縱絲、橫絲、棲息圈，網結好後，簷下姬鬼蛛則在棲息圈或網眼靜候獵物，若發現網上有非生物之異物，則將黏住異物的橫絲弄斷，再把網上的異物丟棄；若網眼被破壞，則會立即修補。收網時間為凌晨2：30 至凌晨6：00，收網時，大部分由第一、二對步足進行收網，偶爾會用最後一對步足將橫絲弄斷，一邊收網一邊將網吞食，收網的順序為：右下、中下、左下、左上、右上，最後留下一條橋絲。簷下姬鬼蛛每天清晨都會收網，並將網吃掉，翌日傍晚再重新結網，其可能原因有兩點：(1)將網吃掉以補充蛋白質。(2)蛛絲容易受灰塵、水氣之污染而減小黏性，降低獵捕功效。簷下姬鬼蛛體長與有效網面積無關，但網的大小視其結網地點寬敞程度而定。體長與網眼、棲息圈面積呈線性關係，表示網眼和棲息圈對簷下姬鬼蛛具有生態或生存意義。我們對簷下姬鬼蛛生態調查之結果，希望能幫助台灣的蜘蛛生態資料庫之建立。