長方體內最少完全城堡數
我們試著尋找所需最小的城堡個數以看守整個a × b × c (a,b,c ? N) 的長方體。所謂城堡是一種棋子，當放置城堡的位置是(x, y, z) ，則(x, y,t)、(x,t, z)、(t, y, z) (t 是任何不超出邊界的正整數)是這個城堡可以看守的格子。我們用這些城堡來完全看守長方體，試著找出其最小值。在2005 年我們猜測了a = b = c 、a = b c 、a > b > c 的上界，而在2006 年時完成了a = b = c 、a = b c 的大部分情況的證明，少數不能解決的部份也提供了不錯的上界。目前我們在a = b = c 、a = b c 的情況幾乎完全解決，目前正在向a > b > c 的部份發展。A generalized searching method of finding the minimum number of castle which can oversee all over the rectangular box, defined as a × b× c (a,b,c ? N) , is presented. The castle here is defined as one kind of chess. The castle positioned as (x, y, z) can direct the lattice points of (x, y,t) 、(x,t, z) 、(t, y, z) (t is the positive integer and smaller than the box size). These castles we use here is to oversee the rectangular box and to help us to find the minimum number. In 2005, we got the upper bound of overseeing the rectangular box in the conditions of a = b = c、a = b c、a > b > c , while in 2006 we complete the proofs of the minimum number of castles based on the conditions of a = b = c 、a = b c . The further work we want to attain is to complete the case of a > b > c.
以簡易方法探討奈米銀的化學活性優於非奈米級銀粒子
A novel and simple method was developed to determine the activity of silver in nanometer particles more than in non-nanometer particles. The conductivity of conducting polymer, polyaniline (PANI) doped with different amount of nanometer silver particles was used to evaluated the activity of nanometer silver. In polymerization of polyaniline, hydrogen chloride solution usually used to increase the conductivity of polyaniline. When 1%(w/w) nanometer silver particles doped during the polymerization, the conductivity of polyaniline was down from 2.28 s/cm to 0.65 s/cm, then increased with increasing the amount of nanometer silver doped. The conductivity of polyaniline was changed from 2.28 s/cm to 0.47 s/cm when 3%(w/w) nanometer silver particles doped, but it is increased from 2.28 s/cm to 2.44 s/cm when was doped with 3%(w/w) micrometer silver particles. The conductivity of polyaniline changed due to the formation of silver chloride (AgCl) in doping nanometer silver. Some of the nanometer silver particles were formed to silver ion in hydrogen chloride solution for the high activity property of nanometer silver. This also can be proved from the spectra of XRD and FE-SEM. Therefore; determination the conductivity of conducting polymer by doping nanometer metal particles can be used to determine the activity of the nanometer particles. 本研究為開發一個新穎的檢測奈米金屬粒子化學活性大於非奈米金屬粒子的簡易方法。方法為利用導電高分子聚苯胺，於合成過程中添加不同濃度的奈米銀粒子，並分別偵測其成品的導電度，藉以評估奈米銀粒子的化學活性。由於聚苯胺在合成過程中通常加入鹽酸以提高其導電度，致活性較大的奈米銀粒子於氧化後，隨即與氯離子形成氯化銀的沉澱，而降低聚苯胺的導電度，如添加1﹪(w/w)奈米銀粒子的，其導電度由2.28 s/cm 降至0.65 s/cm，隨後隨著添加量的增加導電度先降後再稍回升。一般非奈米級銀粒子因氧化電位為負值，即化學活性小，而不易被氧化。由實驗結果，我們發現同樣添加3%(w/w)的奈米級銀粒子或微米級銀粒子，添加奈米級銀粒子的導電度由2.28 下降為0.47，添加微米級銀粒子的導電度卻由2.28 上升為2.44，此乃說明本方法確實足以證明奈米級金屬的化學活性的確遠大於微米級金屬，因相同條件下，微米級銀粒子未如同奈米級銀粒子一樣被氧化成銀離子。即奈米級銀粒子可以輕易的被氧化，而非奈米級銀粒子則不易被氧化。尤其也可由X 光繞射儀分析光譜圖和場發射式掃描電子顯微鏡拍攝圖證明。因此，我們可以採用添加3 %(w/w)奈米級金屬銀粒子及微米級金屬銀粒子於導電高分子的方法，並藉導電度的變化，證明奈米金屬粒子的高活潑性。
以簡易方法探討奈米銀的化學活性優於非奈米級銀粒子
A novel and simple method was developed to determine the activity of silver in nanometer particles more than in non-nanometer particles. The conductivity of conducting polymer, polyaniline (PANI) doped with different amount of nanometer silver particles was used to evaluated the activity of nanometer silver. In polymerization of polyaniline, hydrogen chloride solution usually used to increase the conductivity of polyaniline. When 1%(w/w) nanometer silver particles doped during the polymerization, the conductivity of polyaniline was down from 2.28 s/cm to 0.65 s/cm, then increased with increasing the amount of nanometer silver doped. The conductivity of polyaniline was changed from 2.28 s/cm to 0.47 s/cm when 3%(w/w) nanometer silver particles doped, but it is increased from 2.28 s/cm to 2.44 s/cm when was doped with 3%(w/w) micrometer silver particles. The conductivity of polyaniline changed due to the formation of silver chloride (AgCl) in doping nanometer silver. Some of the nanometer silver particles were formed to silver ion in hydrogen chloride solution for the high activity property of nanometer silver. This also can be proved from the spectra of XRD and FE-SEM. Therefore; determination the conductivity of conducting polymer by doping nanometer metal particles can be used to determine the activity of the nanometer particles. 本研究為開發一個新穎的檢測奈米金屬粒子化學活性大於非奈米金屬粒子的簡易方法。方法為利用導電高分子聚苯胺，於合成過程中添加不同濃度的奈米銀粒 子，並分別偵測其成品的導電度，藉以評估奈米銀粒子的化學活性。由於聚苯胺在合成過程中通常加入鹽酸以提高其導電度，致活性較大的奈米銀粒子於氧化後，隨即與氯離子形成氯化銀的沉澱，而降低聚苯胺的導電度，如添加1﹪(w/w)奈米銀粒子的，其導電度由2.28 s/cm 降至0.65 s/cm，隨後隨著添加量的增加導電度先降後再稍回升。一般非奈米級銀粒子因氧化電位為負值，即化學活性小，而不易被氧化。由實驗結果，我們發現同樣添加3%(w/w)的奈米級銀粒子或微米級銀粒子，添加奈米級銀粒子的導電度由2.28 下降為0.47，添加微米級銀粒子的導電度卻由2.28 上升為2.44，此乃說明本方法確實足以證明奈米級金屬的化學活性的確遠大於微米級金屬，因相同條件下，微米級銀粒子未如同奈米級銀粒子一樣被氧化成銀離子。即奈米級銀粒子可以輕易的被氧化，而非奈米級銀粒子則不易被氧化。尤其也可由X 光繞射儀分析光譜圖和場發射式掃描電子顯微鏡拍攝圖證明。因此，我們可以採用添加3 %(w/w)奈米級金屬銀粒子及微米級金屬銀粒子於導電高分子的方法，並藉導電度的變化，證明奈米金屬粒子的高活潑性。
數位攝譜儀及其數位分析方法
Color is not a physical quantity, but it is a characteristic of spectra. Traditionally spectra of light sources are characterized by the wavelengths and intensities of the spectral lines. We propose an alternative way of charactering spectra using colors. Using digital cameras, convex lens, and a 600 Lines/mm grating, we design a “Digital Spectrophotometer” (Pic.1), which uses no light sensors and electrical circuits that are necessary for conventional spectrometers. To analyze a spectrum using the “Digital Spectrophotometer”, we take digital images of the diffracted light through the grating emitted by the light source and then analyze the intensity distribution of the color components of the spectral lines. The structure of the “Digital Spectrophotometer” is simple and is easy to operate. The Digital Spectrophotometer includes a computer software program we have developed called the “Digital Spectrological Method”. After enlarging the digital spectrographs to a mosaic scale and regards each mosaic as a basic color block, the Digital Spectrological Method will transform every color block into a four dimensional “color coordinates” (λ (wavelength), R(red), G(green), B(blue)), where the coordinateλ is translated from the spatial position of the spectral line and the R, G, and B coordinates specifies respectively the corresponding intensity of the red, green, and blue color components. Comparing the “color coordinates” of the unknown light sources to the known, we can easily identify the wavelengths of the lights emitted by the unknown illuminant precisely. We have accomplished the following experiments by using the “Digital Spectrophotometer”: 1. Measure the spectra of various gaseous atoms, and establish the “database of digital spectra in color coordinates” (DDSCC). 2. Compare the characters of color presentation between digital camera images and positive film of the optical camera. 3. Identify the absorption spectrum of the Solar spectrum (Fraunhofer Lines) using the DDSCC. 4. Analyze the Orion αandβ spectrum using the DDSCC. 5. Identify the 589.0 and 589.6 nm wavelength difference between the “Double Lines of sodium spectrum”. 6. Measure the range of wavelength of the colored LED and register the results into the (λ, R, G, B) coordinates. 7. Compare the range of wavelength of He-Ne Laser and commercial Laser pointer. 8. Measure the Zeeman splitting of the hydrogen atom spectrum at 0.5 Tesla.
顏色雖不是物理量，卻是光譜的特性，傳統上對光譜的分析只記錄波長及對應的強度，而非以顏色來區分。我們運用數位相機、凸透鏡及600 條/㎜光柵，設計一個以顏色成分為標準來分析各類光譜的「數位攝譜儀」(Pic.1)。這個新的設計無須使用傳統光譜儀所需之光感應器及電路設計，只需拍攝光源透過光柵的繞射影像即可分析對應之光譜。我們製作的「數位攝譜儀」包含了一個自行設計的電腦軟體程式「數位光譜分析法」；將拍攝到光譜數位影像放大成「馬賽克」，作為光譜的最小「色塊」，該程式可將每個色塊轉換為一組四維的「顏色座標」 (λ (波長)，R(紅)，G(綠)，B(藍))，其中的λ 座標係由光譜線的位置轉換而來，而紅、綠、藍座標則記錄對應的紅、綠、藍色成分強度。與已知光源譜線的「顏色座標」比較，「數位攝譜儀」可精確測量各種未知光源放射出的光波波長且操作方便。利用「數位攝譜儀」的數位分析方法，我們完成以下實驗：1. 測量不同種類的原子光譜，建立「數位光譜資料庫」，包括氫、汞及鈉原子。2. 比較數位相機影像與光學相機正片的色彩顯影。3. 利用「數位光譜資料庫」，鑑定太陽光譜中的吸收光譜(Fraunhofer Lines)。4. 利用「數位光譜資料庫」，分析獵戶座α、β的可見光光譜。5. 鑑別波長589.0、589.6 奈米的鈉雙線。6. 用顏色座標(λ,R,G,B)測量發光二極體的波長範圍。7. 比較He-Ne 雷射與雷射光筆放光的波長範圍，發現市售雷射光筆所放之光並非單頻。
雪山姑 翡翠嫂 順姑情 逆嫂意? 雪山隧道之地質環評與工程建設的恩怨情仇
實驗初期以膠體水晶模擬岩層，模擬雪山隧道水平傾斜約 1°，製作壓克力模型(實驗一)，證明是否如賈儀平教授所言《雪山隧道＝水脈改道》註3，同時此模型也證明隧道防水襯墊完工後，和隧道開挖時水力梯度的明顯變化。再加上訪問坪林到宜蘭圓通寺一帶居民結論是：1. 雪山隧道對翡翠水庫的影響不大，但對宜蘭方面影響很大2. 模型的數據證明『隧道剛開挖因為出水嚴重出現明顯梯度外，其餘二組都不再有特定梯度，即使隧道處也沒有明顯變化』。證明隧道的水平角度對水也沒有太大導引作用。因為隧道的比例對一座山而言相當小，不會有太大的影響。3. 證明隧道防水襯墊完工後，和施工前(隧道未開挖)是同一狀況。釐清對翡翠水庫影響不大後，重心改為宜蘭。此時我們綜合中興工程資料及地調所資料理出“交錯正斷層的破碎岩體”應是大漏水的原凶！1. 於是用實驗一模型加入“破碎岩體” (實驗二)證明破碎岩體水力梯度的明顯變化。2. 再加上訪問頭城附近社區，了解居民因應大漏水後改變取水層的應變措施。3. 於是再設計模型(實驗三)證明不同不透水層的相互關係。實驗末期再度訪問頭城附近社區，赫然發現水稻已開始種植(去年還荒蕪，居民抱怨連連)看到綠意盎然的稻田和笑逐顏開的居民，我們的照片和實驗數據願為雪山隧道工程做個平反！The experiment began by using gel-crystal model to simulate rock strata and the acrylic model to simulate the dip angle of 1° of the Syue Mountain Tunnel. The experiment aimed to prove if the building of the Syue Mountain tunnel will change the water tunnel as Professor Yi-Ping Jia has indicated. The model also shows the obvious change brought by the membrane lining layed on the Tunnel and the dip angle of the water power gradient when the Tunnel was built. The conclusion of our interiew with residents in the Ping-lin and Yuan-Tong Temple in I-lan is as following: 1. The building of the Syue Mountain Tunnel has more impact on the I-lan than Fei-Tsui Reservoir. 2. The statistics of the model proved that Syue Mountain only showed gradient in the beginning when it was built. The Tunnel itself did not show any obious change. The dip angle of Syue Mountain Tunnel did not draw water due to it is small in size compared to the Syue Mountain. 3. The Syue Mountain Tunnel remained unchanged after the membrane lining was layed. After we can clarify that the Syue Mountain Tunnel has less impact on the Fei-Tsui Reservoir, we turned our attention to I-lan. We combined the information provided by Zhong-Xing Construction and the Central Geological Survey, and found that the cross-normal fault if the cause of the leakage. 1. The second experiement was conducted by adding fractured stones to the previous model and proved these stones will cause the obvious change to the water power gradient. 2. We have conducted another to the communities around Tou-cheng and realized that residents have changed the water supply strata in response to the leakage. 3. Finally, we built another model in 3rd experiment to prove the relationship of 3 water proof stratas. At the end of our experiment, we returned to Tou-Cheng and found that residents have started to grow rice and started to have simle on their face. Our experiment and statistics can do Syue Mountain Tunnel justice.
會逆轉的石頭－RattleBack 逆旋現象
具有長短兩軸的對稱性剛體，譬如半橢球，在施加適當質量配重後，給予其Z 軸方向的 初角速度，將會逐漸上下震盪、搖擺，而後改變原先的角速度方向，朝相反的方向逆轉回來。 此現象稱為「逆旋現象」，本研究分析關於配重、質心距離與表面摩擦係數等因素的影響，利 用光點投影方式判讀其軌跡，並建立數學模型以驗證物理原理。研究發現，動摩擦垂直長軸 的分力所造成的力矩，將會導致逆旋的發生，並且，對本研究的剛體模型而言，加以20g 配 重，與長軸夾45°距質心5.5cm 且動摩擦系數為0.1227 時，逆轉角度有最大值。當長短兩軸 的震盪頻率相近時，甚至會發生兩軸能量的耦合現象，而有不只一次的逆旋。 The phenomenon was found for rigid bodies with long and short symmetrical axes, such as half-ellipsoids. We add extra masses ( Δm ) to a stone of the shape of half-ellipsoid and then give it an initial angular velocity ( 0 ω ) to make it spin. While the stone spins, the two symmetric axes start oscillating up and down. Then, remarkably, the spin of the stone slows down while the amplitude of oscillation increases until the direction of angular velocity reverses. This process is called “Rattle Back Spin-Reversed Phenomenon.” Our study involves the effect of several parameters on the above phenomenon, such as the shape of the stone, the added mass, and the friction between the stone and the table surface. We try to build a physical model to explain the spin-reversed phenomenon which can be recorded by tracing the motion of the stone with optical means. According to our study, the shape of the stone and the distribution of the added mass played crucial roles. The torque generated by kinetic friction along the long axis also helps the spin to reverse. Furthermore, in our experiment, we record a maximum reverse angle with following settings: two sets of 10 grams of mass are symmetrically added to the flat side of half-ellipsoid, in the distance of 5.5 cm to the C.M. of stone and an included 45 degrees angle with a long axis. And the most surprising finding is that when the oscillation frequencies of two symmetric axes are close to each other, the spin of the stone can reverse twice.
在Sapphire 基材上以電化學沉積YAG 螢光薄膜
A novel method of electrolytic Y3Al5O12 (YAG:X, X=Ce, Eu, Tb) phosphor thin-film coating on sapphire was investigated in yttrium, aluminum, cerium, europium and terbium nitrate solution. By means of X-ray diffraction (XRD), scanning electronic microscopy (SEM) observation, and cathodic polarization tests, the most efficient potential of deposition was found in the region between -1.2 V~-1.5 V. The YAG phosphor thin-film was successfully synthesized by the cathodic deposits were heat-treated at 1200 ℃ for 4 hours. The excitation photoluminescence (PL) spectra of Ce3+ in YAG consists of a strong maximum at about λ＝520~530 nm that show yellow emission peak, and a red emission was observed at about λ＝595~700 nm by additional Eu3+. The excitation PL spectra monitored inλ＝480~500 nm with the amount of Tb3+ and that show green emission peak. The fabrication of YAG phosphor thin-film will be useful to improve the emission intensity of the white LEDs in the future.由電解沈積陰極的電位—電流關係圖、Ｘ光繞射分析、SEM 觀察及實驗反應的經驗式我們可以知道要在導電的sapphire（氧化鋁單晶）基材上電解沈積合成燒結YAG 螢光薄膜所需之各類氫氧化金屬，其合適的電解沈積電位為-1.2 Ｖ~-1.5 V，我們利用電化學沈積法可以成功地合成欲燒結成YAG 螢光薄膜所需之氫氧化金屬，將所合成之氫氧化金屬放入高溫爐以1200 ℃高溫燒結4 小時後，依據我們目前以光螢光激發(PL)這些YAG 薄膜的光譜結果，可以成功地得到YAG:Ce(λ=520~530nm)黃光螢光薄膜、YAG:Eu(λ=595~700nm)紅光螢光薄膜及YAG:Tb(λ=480~500nm) 綠光螢光薄膜，證明以新的電化學方法可以成功製備YAG 螢光薄膜，相信這些研究成果未來應用在研發提昇白光LED 發光效能上有極大之助益。