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Metrical properties of functions in terms of various forms of weak differentiability
No full text依循W. Stepanoff、H Whitney及H. Federer的工作，我們研究函數與各種弱性微分有關的量度性質。綜合他們的工作，可知以下四個敘述的等價性：
(1)u在D上幾乎處處幾近可微(approximately differentiable)；
(2)給定ε>0，存在一個定義在R^n上的連續可微函數v，使得u與v相異點所成的集合的測度小於ε；
(3)u的一次差分的幾近上極限(approximate limsup)在D上幾乎處處有限；
(4)u的一階幾近偏導數在D上幾乎處處存在。
接著，W. S. Tai與F. C. Liu把這些結果推廣到更高階(非負整數)的弱性微分性質。我們更進一步地將其推廣到一般階(不限定為非負整數)，證明了以下定理：
主要定理. 對γ>0，以下敘述是等價的：
(1)u在D上擁有γ階Lusin性質；
(2)u在D上幾乎處處γ階Lipschitz連續；
(3)u在D上幾乎處處γ階偏Lipschitz連續。
對於證明主要定理的重要工具─Whitney擴張定理，我們也做了仔細的研究，附加上範數的估計，將定理重新敘述成更容易應用的型式。Metrical properties of measurable functions in terms of various forms of weak differentiability are studied along a line suggested by works of W. Stepanoff, H. Whitney, and H. Federer which can be summarily described as stating that the following four statements are equivalent:
(1) u is approximately differentiable a.e. on D.
(2) Given epsilon > 0, there is a C^1 function v on R^n such that |{x in D : u(x) does not equal v(x)}| < epsilon.
(3) ap-limsup_{y tends to x}|u(y)-u(x)|/|y-x|< ∞ for almost all x ∈ D.
(4) First order approximate partial derivatives of u exist a.e. on D.
W. S. Tai and F. C. Liu then generalize the results to the situation involving higher (integral) order of weak differentiability. For a further generalization to fractional order, we prove the following theorem:
Main Theorem. For gamma > 0, the following statements are equivalent:
(1) u has Lusin property of order gamma on D.
(2) u is approximately Lipschitz continuous of order gamma
at almost every point of D.
(3) u is partially approximately Lipschitz continuous of order gamma at almost all point of D.
Whitney’s Extension Theorem, which is a main tool for the proof of the Main Theorem, is also given a detailed consideration and reformulated in a form with appropriate norm estimates. This form seems to be of a final touch and can be applied more effectively
Inverted top-emitting organic light-emitting devices with an effective cathode structure
No full textA Three-Axis Flexible Tactile Sensing Array Based on Novel Capacitance Mechanism
No full text本研究提出一創新性電容感測器結構設計，發展出三軸向可撓性觸覺感測陣列，將應用於仿生機器人之人工皮膚，以實現機器人具有抓握物體的能力。此感測器結構的設計，除了製造程序簡易，更具有高可靠度的特性。本研究中，電容感測陣列的製造技術，是採用微機電製程及軟性電路板技術製作而成，其感測元件以聚二甲基矽氧烷 (Polydimethylsiloxane, PDMS) 與聚亞醯胺 (Polyimide, PI) 構成其主要結構材質。其中PDMS結構層型是由微機電技術之微影製程製作SU-8母模所翻模而成。並於PDMS結構層上，蒸鍍已定義圖形之金屬層，來作為電容式感測陣列當中之浮動電極。感測電極與金屬導線則利用軟性電路板技術製作完成。在每一個三軸向觸覺感測單元當中，則有四個電容感測器，能將接觸力轉換成正向力與剪力。為了能更精準偵測剪力變化，在研究中，將凸塊結構與觸覺感測器之間的支撐圓柱應用於其中。本研究針對所製作感測器單元進行三軸向的特性量測，其敏感度分別為X軸方向 1.72%/mN、Y軸方向 1.65%/mN 與Z軸方向1.1%/mN。其感測單元能有效量測力量範圍為100mN。研究中亦開發32×32電容式觸覺感測陣列之掃描電路，將其應用於所相對應的感測器陣列。In this work, we present the development of a capacitive normal and shear sensing array realized by using MEMS fabrication techniques and flexible printed circuit board (FPCB) technologies. The sensing array, which consists of two micromachined polydimethlysiloxane (PDMS) structures and a flexible FPCB, will be used as the artificial skin for robot applications. The shear sensing element, which comprises four capacitive sensing elements arranged in a 2?2-array form, can decompose the contact force into normal and shear components. Each capacitive sensing element has two sensing electrodes and a common floating electrode. The sensing electrodes as well as the metal interconnect for signal scanning are implemented on the FPCB, while the floating electrode is patterned on one of the PDMS structures. This special design can effectively reduce the complexity of device structure and thus makes the device highly manufacturable. In order to accurate detect shear force, the bump and the pillar structures of each shear sensing element are implemented. An 8?8 shear-stress sensing array been realized. Each sensing element can detect normal and shear stresses applied on its top surface. The average measured sensitivity for the normal stress (i.e., the z-direction) is 1.1%/mN, and average measured sensitivities are 1.72%/mN, 1.65%/mN in the x and y-directions, respectively. Measurement of a single sensor shows that the full-scale range of detectable force is about 100 mN. The corresponding scanning circuit are also designed and implemented.致謝 I要 IIbstract I錄 II目錄 IV目錄 VII號說明 VIII一章 緒論 1.1 前言 1.2 研究動機與目的 2.3 文獻回顧 3.3.1 壓阻式觸覺感測器 3.3.2 壓電式觸覺感測器 9.3.3 電容式觸覺感測器 11.3.4 其他類型觸覺感測器 16.4 論文架構 19二章 感測原理與元件設計 20.1 電容式感測基本原理 20.2 浮動電極電容感測機制 24.3 三軸向電容感測器結構設計與感測原理 27三章 製造方法與步驟 36.1 製程規劃 36.2 製程設計與原理 37.2.1 基材清潔 39.2.2 微影製程 39.2.3 金屬蒸鍍 41.3 感測器之製作流程 42.3.1 SU-8母模製程 42.3.2 PDMS轉印製程 46.3.3 E-beam鍍膜 50.3.4 PDMS之氧氣電漿接合 52四章 量測結果與討論 58.1 實驗平台架設 58.1.1 三軸移動平台 59.1.2 拉壓力計 60.1.3 線性規 61.1.4 電容量測儀器 62.2 32×32電容式掃描電路設計與製作 65.3 三軸向電容式感測單元效能量測與分析 68五章 結論與未來展望 74.1 結論 74.2 未來展望 76考文獻 7
Electromagnetic Simulation and Fabrication of Novel Organic Light-Emitting Devices
No full text由於有機發光二極體元件可以做為高效率、大面積及全彩的顯示器應用，近年來受到廣泛的研究及討論。在有機發光二極體元件中，許多元件結構的光學效應會很嚴重影響元件的效能。在這論文中，我們用古典電磁學去模擬及分析典型有機發光二極體、上發射型有機發光二極體及光學微共振腔有機發光二極體的發光特性。
上發射型有機發光二極體應用於主動矩陣有機發光二極體顯示器有很多技術上的長處。然而，上發射型有機發光二極體固有的強光學共振腔效應將會複雜化元件效率及其他視角特性的優化條件。在這博士論文中，我們提出一個上發射型有機發光二極體做為顯示器應用時，優化其視角特性的方法論。這分析跟方法論的有效性也經由實驗結果驗證了。
接下來，我們有系統地分析利用兩金屬電極形成光學微共振腔的有機發光二極體的光學特性。分析的結果顯示，若要從光學微共振腔元件得到比傳統元件較高的發光效率，需要有高反射的背反射鏡面以及低吸收、高反射的出口鏡面。同時，也利用嚴謹的電磁學模型，分析研究共振波長對於光學微共振腔發光特性的影響。
由於一般來說有機材料的低傳導特性及低載子傳輸能力，有機發光二極體的優化條件，都是將發光位置設計在反射金屬電極的第一個反節點位置附近。在這論文中，利用有包含傳導摻雜的元件結構，我們在理論上以及實驗上研究相對於金屬電極的發光位置對於發光特性的影響。分析結果顯示，若將發光位置放在接近第二個反節點附近，將可以得到1.2倍的整體出光量的增加，以及1.6倍的正向發光效率的增加。取決與細部條件，第二個反節點的元件也許有如強光學微共振腔中經常觀察到的更指向性的發光，但是沒有嚴重地隨視角變化的顏色飄移的問題。Organic light-emitting devices (OLEDs) have been the subjects of intense investigation in recent years due to their applications in efficient, large-area and full-color displays. In OLEDs, the optical effects of various device structures are critical to device performances. In this thesis, we use the classical electromagnetic theory to model and analyze the emitting characteristic of typical OLEDs, top-emitting OLEDs, and microcavity OLEDs.
Top-emitting organic light-emitting devices (OLEDs) have a few technical merits for active-matrix OLED displays. Generally stronger microcavity effects inherent with top-emitting OLEDs however complicate optimization of device efficiency and other viewing characteristics, such as colors and viewing-angle characteristics. In this thesis, a general methodology for optimizing viewing characteristics of top-emitting OLEDs for display applications is suggested. The effectiveness of the analysis and the methodology is confirmed by experimental results.
Next, optical characteristics of microcavity organic light-emitting devices (OLEDs) having two metal mirrors are systematically examined. Analyses show that a high-reflection back mirror and a low-loss high-reflection exit mirror are essential for such microcavity devices to obtain luminance enhancement relative to conventional noncavity devices. The effects of resonant wavelengths on performances of microcavity organic light-emitting devices by using the rigorous classical electromagnetic model are also examined.
Due to generally low conductivity and low carrier mobilities of organic materials, organic light-emitting devices (OLEDs) are typically optimized for light outcoupling by locating emitters around the first antinode of the metal electrode. In this thesis, by utilizing device structures containing conductive doping, we investigate theoretically and experimentally the influences of the location of emitters relative to the metal electrode on OLED emission, and show that substantial enhancement in light outcoupling (1.2 times) or forward luminance (1.6 times) could be obtained by placing emitters around the second antinode instead of the first antinode. Depending on the detailed condition, the second-antinode device may also give more directed emission as often observed in strong-micrcavity devices yet without suffering color shift with viewing angles.Chapter 1 Introduction of Organic Light-Emitting Devices
1.1 General overview of OLED devices and displays 1
1.2 Microcavity effects in OLED devices 3
1.3 Thesis organization 6
References 9
Figures 12
Chapter 2 Optical Modeling of Organic Light-Emitting Devices
2.1 Introduction 15
2.2 Theory 16
2.1.1 Fundamental theory 16
2.1.2 Optical model of OLED 21
References 30
Figures 32
Chapter 3 Analyzing and Tuning Emission Characteristics of
Top-Emitting Organic Light-Emitting Devices
3.1 Introduction 37
3.2 Device Structures 38
3.3 Simulation and Analysis 40
3.4 Methodology for Optimizing Viewing Characteristics of Top-Emitting OLEDs 45
3.5 Experimental Results 47
3.6 Summary 49
References 51
Figures 53
Chapter 4 Examining Microcavity Organic Light-Emitting
Devices Having Two Metal Mirrors
4.1 Introduction 65
4.2 Simulation and Analysis 66
4.3 Experimental Results 72
4.4 Summary 75
References 76
Figures 78
Chapter 5 Examining Effects of Resonant Wavelengths on
Performances of Microcavity Organic Light-Emitting
Devices
5.1 Introduction 89
5.2 Simulation and Analysis 90
5.3 Experimental Results 95
5.4 Summary 97
References 99
Figures 101
Chapter 6 Enhancing Light Out-coupling of Organic Light-
Emitting Devices by Locating Emitters at Farther Antinodes of the Reflective Metal Electrode
6.1 Introduction 105
6.2 Simulation and Analysis 107
6.3 Experimental Results 111
6.4 Summary 114
References 115
Figures 117
Chapter 7 Summary and Future Directions
7.1 Summary 124
7.2 Future Directions 125
References 127
Appendix 128
List of SCI Journal Publication (Chun-Liang Lin
The Purification and Characterization of Protein Phosphatase from Sweet Potato Roots
No full text可逆性的蛋白質磷酸化，是細胞常見的訊息傳導機制之一；藉由蛋白質激脢與磷酸脢相互拮抗的磷酸化活性來調控。本論文以甘藷塊根為材料，利用硫酸銨分劃、親合層析、離子交換層析、膠體過濾層析等純化步驟，得到四類不同的磷酸脢，且分別命名為 P I, P II, P III, P IV。其中 P II經由定序結果得知為一甘藷體內的酸性磷酸脢。藉由不同基質的磷酸脢活性分析結果，與以放射線磷酸標定之磷酸化 L-SP為基質的活性分析結果比對，發現純化所得之四類磷酸脢雖然對其他基質具有高度活性，但無法對磷酸化 L-SP進行去磷酸化反應。添加金屬離子作為 cofactor或加入抑制劑也無法觀察到對磷酸化 L-SP進行去磷酸化的活性改變。推測甘藷塊根在此一生長時期，無對磷酸化 L-SP具專一性之磷酸脢存在。The reversible phosphorylation/dephosphorylation of protein is one of the common but important cell regulation mechanisms in the cell. The L-form starch phosphorylase from sweet potato root could be phosphorylated by LSK in vitro. In this study, we partially purified four phosphatases by ammonium sulfate fractionation, ion exchange, gelfiltration, and affinity chromatography, and termed PI, PII, PIII, and PIV. PII was shown to be a purple acid phosphatase. Differences in pH optima, phosphatase inhibitors, and response to divalent cations indicate that these phosphatases showed no dephosphorylation activity on the phosphorylated L-SP, which was phosphorylated by LSK. Those results were indicated that the sweet potato roots in this stage might be no related phosphatase to dephosphorylate L-SP.中文摘要 3
Abstract 4
縮寫表 5
第一章 前 言 7
1.1 澱粉磷解脢 7
1.1.1 澱粉磷解脢 7
1.1.2 澱粉磷解脢的分類 7
1.1.3 分子序列及構形比對 7
1.1.4 L-SP上L78分子序列的特異性 8
1.2 蛋白質的磷酸化與去磷酸化反應 12
1.2.1 蛋白質激脢 13
1.2.2 蛋白質磷酸脢 13
1.3 研究動機 17
第二章 材料與方法 25
2.1 電泳檢定法 25
2.1.1 原態膠體電泳 25
2.1.2 SDS膠體電泳 28
2.1.3 製備式電泳與電泳溶離 30
2.1.4 膠片染色法 31
2.1.5 膠片乾燥法及護貝 33
2.1.6 蛋白質電泳轉印法 34
2.1.7 膠體內蛋白質水解 36
2.2 一般分析法 37
2.2.1 蛋白質定量 37
2.2.2 甘藷塊根澱粉磷解脢 L-SP活性分析法 38
2.2.3 甘藷磷酸脢活性分析法 (1) 以pNPP為基質 39
2.2.3 甘藷磷酸脢活性分析法 (2) 以L-SP及 L-78為基質 40
2.3 管柱色層分析法 41
2.3.1 管柱色層層析法之基本操作 41
2.3.2 膠體澎潤法及前處理 43
2.3.3 膠體過濾法 44
2.3.4 離子交換法 44
2.3.5 疏水性層析法 45
2.3.6 親和性層析法 46
2.4 酵素粗抽取及硫酸銨分劃 47
儀器設備： 47
藥品試劑： 48
方法步驟： 48
2.6 甘藷塊根澱粉L型磷解脢純化法 49
儀器設備： 49
藥品試劑： 49
方法步驟： 49
2.7 甘藷塊根澱粉L型磷解脢激脢純化法 50
儀器設備： 50
藥品試劑： 50
方法步驟： 50
2.8 甘藷塊根磷酸脢純化法 50
儀器設備： 50
藥品試劑： 51
方法步驟： 51
第三章 結果與討論 53
3.1 甘藷塊根中具有磷酸脢 53
3.2 蛋白質磷酸脢部分純化 53
3.2.1 酵素粗抽取 53
3.2.2 硫酸銨分劃 53
3.2.3 Phosphocellulose親和層析法 54
3.2.4 陰離子交換層析 (Ion-exchange chromatography) 54
3.2.5 P I之進一步純化 54
3.2.6 P II之進一步純化 55
3.2.7 P III之進一步純化 55
3.2.8 P IV之進一步純化 55
3.3 去磷酸化條件測試 56
3.4 Imidazole 對磷酸脢活性影響 56
3.5 LC-Mass-Mass定序結果 57
第四章 結 論 81
參考文獻 8
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