Now Artificial Neural Networks using on the basic math is fewer. This paper is to suggest the Linear equation of the basic math using the BP Artificial Neural Networks. The BP Neural Networks have power ability for learning and can approximate any function, and regularity can be found to solve the linear equation. A good sample is one of the important elements for learning of Artificial Neural Networks. Generally, the samples are a lot of amount for the resolution of Linear equation. This paper is to use the principle of two points decide one line for the samples. The experiment shows that this method curtails many samples. Furthermore we also use Artificial Neural Networks to solve the problem of point-slope form. The experiment result is very satisfactory, and it offers some idea for the basic math using Artificial Neural Networks.目前人工神經網路較少用於基礎數學方面的求解，本文針對基礎數學直線方程式提出BP 人工神經網路應用於求解直線方程式，運用其很強的學習能力、(輸入向量和其對應的目標向量來訓練網路、逼近函數)，尋求規律來求解直線方程式；而良好的樣本是人工神經網路學習的重要條件之一，一般解決直線方程式需要大量樣本，本文利用二點決定一直線的原理來解決樣本問題，實驗結果顯示，這一方法成功的縮短了可觀的學習樣本，此外我們也運用BP 人工神經網路來求解點斜式的直線方程式問題，實驗結果是可行的，並且為人工神經網路用於基礎數學提供了一些思考方向。

動脈硬化是個致病率和致死率相當高的慢性發炎疾病，為台灣十大死因之一。在病理過程中血中濃度過高的膽固醇為動脈硬化的一大危險因子，其會誘發一連串的發炎反應驅使血管壁內皮細胞功能喪失，血壓上升，平滑肌細胞增生等。Statin 是臨床上十分有效的降血脂藥物，雖然其作用機制已知在於抑制膽固醇合成酵素 HMG-CoA reductase 而有降血脂功效，但近年來探討 statin 在抗發炎方面的作用也漸受重視。nitric oxide synthase (NOS) 代謝產物如 nitric oxide (NO)，cyclooxygenase (COX) 代謝產物如 prostaglandin (PGE?、PGI?)，及 heme oxygenase-1 (HO-1) 代謝產物如 carbon monoxide (CO)，均有文獻指出可以改善血流，而可能在動脈硬化上扮演保護角色。相反的，matrix metalloproteinase (MMP) 的表現會誘使更多的免疫細胞浸潤到血管壁，並增加動脈硬化斑破裂，引起栓塞和中風的發生。在此實驗中，我們利用培養的大鼠主動脈血管平滑肌細胞作為研究材料，發現了 statin (lovastatin 、pravastatin、atorvastatin 、fluvastatin) 具有一些和降血脂無關的直接保護血管壁能力。包括會增加 interleukin-1β (IL-1β) 所誘導 iNOS 蛋白的表現及NO 的產生; statin 本身會增加 COX-2 和 HO-1 蛋白的表現及 PGE? 和PGI? 的產生，及抑制 MMP-2 和 MMP-9 蛋白活性的表現。此外分析調控 iNOS 基因轉錄最為關鍵的基因轉錄因子 NF-κB，發現適量的 statin 會增加 IL-1β 活化NF-κB 的作用。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。為更進一步釐清 statin 是否會影響受細菌感染病人的生命危險，我們也探討 statin 對LPS 作用的影響。結果發現 statin 反而會抑制 LPS 誘導大量 iNOS 蛋白的表現，NO 的產生及 NF-κB 的活化。這些新的實驗結果提供更多證據支持 statin 可以藉由維持血管舒張，減緩血管壁的發炎反應，穩定動脈硬化斑的作用，以有效控制動脈硬化各個病程的進展。這發現能讓我們更透徹明白 statin 的作用，且對將來研發 statin 在心血管疾病方面新的臨床治療用途是有所助益的。 ;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. In this study, we investigated the effects of lovastatin, pravastatin, atorvastatin, and fluvastatin on cultured rat vascular smooth muscle cells. We found statins can inhibit LPS-induced iNOS expression and NO production, while they can potentiate IL-1β-elicited responses. Moreover, statins themselves can stimulate COX-2 expression, PGE?, PGI? formation, and HO-1 induction. In contrast, statins can inhibit basal and IL-1β-induced enzyme activities of MMP-9 and MMP-2. In studying the activity of NF-κB, which plays an important role for iNOS gene induction, we found that statin can increase IL-1β-induced NF-κB activity, while inhibit that induced by LPS. All these results suggest that stimulation of iNOS expression in the presence of IL-1β, togeth1er with the increased COX-2 and HO-1 expression might contribute to the beneficial effects of statins in atherosclerotic process in terms of vasodilation and inhibition of smooth muscle cell proliferation. The inhibition of MMP activity might enhance plaque stability and reduce the development of atherosclerosis. All these results strengthen the pleiotropic actions of statins in anti-inflammation and anti-atherosclerosis.

Two soldiers walk on a checkerboard. They can only walk one step once a time and two directions, front and left, are decided randomly. The gunshot is the column and row where a soldier is located, and one will die if he enters the gunshot area of the other. To treat the probability of winning, we first study the cases of 1×n, 2×n, 3×n, and 4×n rectangles iterately. Then we establish a general form of the probability of winning in a general n×k rectangle by using recurrence technique and generating function, respectively. Finally, we extend to the general n×m×k cuboid case to obtain the first soldier’s probability of winning.在一個長方形的棋盤中，兩士兵行走，每一次只走一步，而且上和左兩個方向是隨機的，射程範圍是所在的此行和此列，而進入他人射程範圍則死亡。探討其獲勝機率，從1×n 、2×n、3×n、4×n 矩形的情形逐步研究，並分別運用遞迴式的技巧及生成函數，導出 n×k 矩形中先走士兵獲勝機率的一般式。更進一步地，我們也獲得了n×m×k 立體空間先走士兵的獲勝機率。

打開水龍頭，水鉛直落到正下方的水平板時形成圓形水躍。我們實驗研究20＜Nr＜150 的低雷諾數圓形水躍的變因，探討圓形水躍半徑和流量、出水口高度、以及液體黏滯係數間的關係。改用高黏滯係數的液體（4：1 的乙二醇水溶液），鉛直落入板上方深h 的相同液體時，先形成圓形，h 漸大時形成環形圓紋曲面，再加大h，形成多邊形水躍，內外圍同方向旋轉，轉速ω；液中加水，黏滯係數高於及低於某定值，多邊形都消失，側面觀察，外圍液體作鉛直面旋轉。將水平板改置於旋轉盤上方，使高黏滯係數（4：1）的乙二醇水溶液鉛直落入板上方形成多邊水躍，逐漸加快旋轉盤的轉速至 ω 時，多邊形都消失；逐漸減少乙二醇的濃度，至完全用水實驗，亦有多邊形出現，我們認為；平板上方的液體的轉動是非圓形水躍的成因。When a jet of water falls vertically on to a horizontal plate, it spreads out rapidly in a thin layer until it reaches a critical radius at which the layer depth increases abruptly. This phenomenon commonly called the circular hydraulic jump. We study the variations of the circular hydraulic jump radius, as a function of volume flow rate of the jet, the drop height, and the viscosity of the fluid at low Reynold numbers (20＜Nr＜150). When a jet of ethylene-glycol mixed with water (the kinetic viscosity is 10 times of water) falls on to a horizontal plate which is immersed in the same liquid with height h. We find the circular state frequently undergoes spontaneous breaking at its axial symmetry into a stationary polygonal shape. Rather than displaying the weak angular deformation generally seen in fluids, the jump forms clear corners and edges that are often straight. Several of these polygon formations show consistency in height h. And we find the polygon structure rotates in a horizontal motion. When a jet of water falls on to a horizontal plate, and the plate is rotated by a motor ,we find the axial symmetry of the free surface of circular hydraulic jump is spontaneously broken a various number of cornered polygonal shapes. We study the number of corners as a result of the volume flow rate of the jet, the drop height and the viscosity of the fluid in the experiment. And the frequency of rotation of the plate is taking into consideration.

Lotus self-cleaning effect arises because the leaves have the superhydrophobic surfaces. When rain falls onto a lotus leaf, water beads up as a result of surface tension. The water drops promptly roll off the surface, taking every dirt with them. This phenomenon is called the lotus effect. With the aid of a light microscope and an Environmental Scanning Electron Microscope, we observe and describe the morphology of the leaves of Nelumbo nucifera in detail. We successfully observe the real interface between air, water droplets and the papillae of a lotus leaf, and find the evidence of a composite surface that is formed by epicuticular wax crystals and air. These observations improve our understanding of the two-level composite surfaces that are formed by micro-scale papillae, nano-scale epicuticular wax crystals and air. We try the method of using the critical angle of a static drop beginning to roll on inclined surface to evaluate the self-cleaning ability. We then find out that it may be a more precise criterion compared to using the static contact angle for the evaluation of the lotus effect. Literature review shows that the earlier investigation lacks the height(H) and interval(I) of the projections on the lotus leaf surface. A close relationship between the self-cleaning property and the H/I ratio is found. In this study, we present the experimental data of the height and interval of the projections on four different species of plant leaves that all have lotus effect, which may be of great help to technological applications. 蓮花效應是指蓮葉表面具有超疏水性與自我潔淨的能力，當雨水落在葉面，因為表面張力的作用形成水珠，水滴迅速滾離葉面，把灰塵一起帶走。本實驗以光學顯微鏡和環境式掃描式電子顯微鏡觀察蓮葉，詳細描述其表面形態，成功的發現空氣、水滴和蓮葉乳突真實的接觸界面以及表面蠟和空氣構成複合表面的證據。實驗結果可以使乳突、奈米表面臘質和空氣構成的雙層次複合表面更容易被了解。我們嘗試以水滴傾斜滾動臨界角來評估自潔能力強弱，實驗結果比傳統使用靜止接觸角更為準確。表面高度和間距的比值與蓮花效應有很大的關係，查閱文獻顯示蓮葉缺乏這些資料，本研究提出四種有自潔能力的葉子的實驗數據，這些數據應該對科技應用有很大的幫助。

Hamiltonian和Hiroimono路徑問題都有百年以上的歷史，且沒有直接解決方法，可能因為是題目本身的條件在討論時尚不足解決問題，現階段只能用電腦去跑。

如果將各種形狀不一的中空框架放入肥皂水中，框架上會結構出不同形式的\r 肥皂膜。本研究中包含了許多不同的實驗以探討各種常見錐體、柱體的肥皂膜形\r 狀，其邊數對肥皂膜面數的影響，及肥皂膜面積和模型邊長的比例關係。\r 第一部分的實驗中，我們探討不同的溶液、不同濃度對形成肥皂膜面數、模\r 式的影響；第二部分的實驗討論了n 角錐所形成的肥皂膜模式，並且得到其形成\r 的肥皂膜面數與角錐邊數n 存在著「肥皂膜面數= 3n - 3 」的關係；第三部分的實\r 驗討論了n 角柱所形成肥皂膜的模式，得到肥皂膜面數與柱體邊數n 存在著「肥\r 皂膜面數= 3n +1」的關係，其中三角柱為例外，一共只形成九面肥皂膜；第四部\r 分則討論了正八面體等其他形狀的模式；第五、第六部分的實驗則分析了肥皂膜\r 的大小與框架比例間的關係。

在一個有障礙的平面上，給三個定點，我們探討連接此三點的最佳網絡。我們討論了諸如直線、射線、線段、圓、網格狀、三角形……等類的障礙，當網絡每穿越障礙一次，就必須付出代價，例如「拖延5 分鐘」。所以，設網絡穿越障礙的次數為y ，則網絡除了原本的總長度之外，還額外加入y 倍某固定數值的損耗。我們以費瑪點的各種性質及三角形不等式等方法為工具，就不同的穿越障礙次數綜合比較，而找出最佳網絡。在某些情況下，最佳網絡不是以費瑪點來連接三點，而是在障礙(如：直線)上找出符合某種與餘弦值相關特殊性質的點，以該點來連接三點，而此網絡可用GSP 軟體相當精確地作出。另外，我們也探討在考慮障礙造成損耗的情況下，兩點間的「實際距離」為何。 最後，我們考慮「混合障礙」問題。在此類問題中，除了前面所討論的障礙，還另加了如同「河流」的兩平行直線間區域之障礙，在這種障礙區域中，網絡的長度要乘以數倍來計算。我們發現，此類問題的最佳網絡也可用特定的正弦條件配合GSP 而相當精確地作出來。;Considering various kinds of obstacles in a plane, such as a line, a segment, a ray, a circle, a triangle or chessboard grids, which function like a red light, we research into the problem of finding the optimal network connecting three given points A, B, C in the plane amidst obstacles described above. Each time when the network crosses an obstacle, it will cause losses, such as five minute’s delay or a loss of one hundred dollars. Taking advantage of Fermat points, some basic inequalities concerning triangles and some special qualities about sine or cosine functions, we obtain the optimal networks in different situations. Besides, we consider what the “real distance” between two points is when there are obstacles in a plane. We also put another obstacle, including a line and a weighted region between two parallel lines, into consideration. In the region, like a river or a muddy ground in real life, the length of the network should be multiplied by a fixed time. Furthermore, we can use GSP to make the networks very accurately.

用塑膠軟管作為氫爆安全反應器，從封閉端點燃氫氧預混氣，管中火焰\r 傳遞快速，肉眼難以觀察，因此研製「氣爆顯影記錄器」來觀測，如下圖，\r 光纖導引偵測點的火光至暗箱，記錄於高速旋轉的軟片，從光電轉速計讀取\r 轉速，軟片沖洗後量測各顯影間距，可得火焰位置與時間的關係圖，量測時\r 間最小刻度可達2. 2 微秒。\r 解讀軟片的顯影，得知氫爆初期，火焰加速傳遞，大部分在25cm 位置\r 左右，火焰的速率出現急速飆升(爆燃轉變為爆震)，而且火光亮度也急速升\r 高，有時火焰速率出現飆升過高，再回降趨於穩定?的現象，在50 cm 位置\r 左右，火焰進入等速傳遞階段，此階段有穩定的火焰模型，火焰頂端的亮度\r 最高，往後亮度遞減。

Based on environmental protection and new energy development, the energy containing low pollution and having high efficiency becomes more popular. The fuel cell is an emerging technology, which is the reason why it is considered as Green energy. However, high-price membrane electrode assembly (MEA) inhabits the development of fuel cell. Among these components in MEA, platinum-based electrode leads the most cost. We select the multi-walled carbon nanotubes (MWNTs) as catalyst support to improve electrode material performance and reduce Pt utilization. But the particle size and dispersion of platinum as well as character of catalyst support may significantly affect the efficiency of electrode.燃料電池因為具備低排放污染、低噪音及高轉換效率等環保特性，故被稱為綠色能源，可取代內燃機作為發電之能源系統。然而燃料電池中觸媒粒徑大小、分散情形以及使用不同的觸媒載體，均有可能會影響其電觸媒的催化效能，所以我們以「觸媒粒徑大小」、「觸媒分散情形」為主軸，著手以下的研究。本實驗在不同的酸鹼值下製備燃料電池的電極材料，並以電子顯微鏡等器材，觀察已披覆在電極上白金觸媒的特性，探討不同酸鹼環境對白金觸媒粒徑大小的影響，並探究白金觸媒粒徑大小與其發電效率的關係。