The usual practice in any discussion of an inner-product space is to restrict the field over which the inner-product space is defined to the field of complex numbers. In defining the inner-product function, (x,y), a second function is needed; namely the conjugate function (x,y)* so that (x,y) ± (y,x)*. We will attempt to generalize this concept by investigating the existence of a conjugate function defined on fields other than the field of complex numbers and relate this function to an inner-product function defined on a linear space L over these fields.

This thesis is a study of some axioms and theorems, and product spaces.

This thesis is a study of fundamental properties of Hilbert space, properties of linear manifold, and realizations of Hilbert space.

by Tong Shiu Sing Dominic. / Parallel title in Chinese characters. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 236-241). / Acknowledgements --- p.iv / Abstract --- p.v / Chapter 1 --- Open Systems and Quasinormal Modes --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.1.1 --- Non-Hermitian Systems --- p.1 / Chapter 1.1.2 --- Optical Cavities as Open Systems --- p.3 / Chapter 1.1.3 --- Outline of this Thesis --- p.6 / Chapter 1.2 --- Simple Models of Open Systems --- p.10 / Chapter 1.3 --- Contributions of the Author --- p.14 / Chapter 2 --- Completeness and Orthogonality --- p.16 / Chapter 2.1 --- Introduction --- p.16 / Chapter 2.2 --- Green's Function of the Open System --- p.19 / Chapter 2.3 --- High Frequency Behaviour of the Green's Function --- p.24 / Chapter 2.4 --- Completeness of Quasinormal Modes --- p.29 / Chapter 2. 5 --- Method of Projection --- p.31 / Chapter 2.5.1 --- Problems with the Usual Method of Projection --- p.31 / Chapter 2.5.2 --- Modified Method of Projection --- p.33 / Chapter 2.6 --- Uniqueness of Representation --- p.38 / Chapter 2.7 --- Definition of Inner Product and Quasi-Stationary States --- p.39 / Chapter 2.7.1 --- Orthogonal Relation of Quasinormal Modes --- p.39 / Chapter 2.7.2 --- Definition of Hilbert Space and State Vectors --- p.41 / Chapter 2.8 --- Hermitian Limits --- p.43 / Chapter 2.9 --- Numerical Examples --- p.45 / Chapter 3 --- Time-Independent Perturbation --- p.58 / Chapter 3.1 --- Introduction --- p.58 / Chapter 3.2 --- Formalism --- p.60 / Chapter 3.2.1 --- Expansion of the Perturbed Quasi-Stationary States --- p.60 / Chapter 3.2.2 --- Formal Solution --- p.62 / Chapter 3.2.3 --- Perturbative Series --- p.66 / Chapter 3.3 --- Diagrammatic Perturbation --- p.70 / Chapter 3.3.1 --- Series Representation of the Green's Function --- p.70 / Chapter 3.3.2 --- Eigenfrequencies --- p.73 / Chapter 3.3.3 --- Eigenfunctions --- p.75 / Chapter 3.4 --- Numerical Examples --- p.77 / Chapter 4 --- Method of Diagonization --- p.81 / Chapter 4.1 --- Introduction --- p.81 / Chapter 4.2 --- Formalism --- p.82 / Chapter 4.2.1 --- Matrix Equation with Non-unique Solution --- p.82 / Chapter 4.2.2 --- Matrix Equation with a Unique Solution --- p.88 / Chapter 4.3 --- Numerical Examples --- p.91 / Chapter 5 --- Evolution of the Open System --- p.97 / Chapter 5.1 --- Introduction --- p.97 / Chapter 5.2 --- Evolution with Arbitrary Initial Conditions --- p.99 / Chapter 5.3 --- Evolution with the Outgoing Plane Wave Condition --- p.106 / Chapter 5.3.1 --- Evolution Inside the Cavity --- p.106 / Chapter 5.3.2 --- Evolution Outside the Cavity --- p.110 / Chapter 5.4 --- Physical Implications --- p.112 / Chapter 6 --- Time-Dependent Perturbation --- p.114 / Chapter 6.1 --- Introduction --- p.114 / Chapter 6.2 --- Inhomogeneous Wave Equation --- p.117 / Chapter 6.3 --- Perturbative Scheme --- p.120 / Chapter 6.4 --- Energy Changes due to the Perturbation --- p.128 / Chapter 6.5 --- Numerical Examples --- p.131 / Chapter 7 --- Adiabatic Approximation --- p.150 / Chapter 7.1 --- Introduction --- p.150 / Chapter 7.2 --- The Effect of a Varying Refractive Index --- p.153 / Chapter 7.3 --- Adiabatic Expansion --- p.156 / Chapter 7.4 --- Numerical Examples --- p.167 / Chapter 8 --- Generalization of the Formalism --- p.176 / Chapter 8. 1 --- Introduction --- p.176 / Chapter 8.2 --- Generalization of the Orthogonal Relation --- p.180 / Chapter 8.3 --- Evolution with the Outgong Wave Condition --- p.183 / Chapter 8.4 --- Uniform Convergence of the Series Representation --- p.193 / Chapter 8.5 --- Uniqueness of Representation --- p.200 / Chapter 8.6 --- Generalization of Standard Calculations --- p.202 / Chapter 8.6.1 --- Time-Independent Perturbation --- p.203 / Chapter 8.6.2 --- Method of Diagonization --- p.206 / Chapter 8.6.3 --- Remarks on Dynamical Calculations --- p.208 / Appendix A --- p.209 / Appendix B --- p.213 / Appendix C --- p.225 / Appendix D --- p.231 / Appendix E --- p.234 / References --- p.236

本文以勞動市場基本供需架構，利用行政院主計處人力運用調查資料，探討台灣地區工資結構與工資差異之變化。由基本資料分析發現，不同教育程度間的工資差異持續縮小，而此極現象主要來自供給面與需求面的變動。 在實証上，採用內積(inner product)法、分解(decomposition)法、及特徵根與特徵向量(eigenvalue and eigenvector)法分析發現，供給面之變勁主要是由於教育普及，人人追求高學歷，導致低教育程度者供給減少，高教育程度者供給增加，而此極變動是造成國中、高中程度中工作經驗屬於兩端者與高職、專科、大學程度中工作經驗屬於中間者工資差異縮小的主要因素：前者供給減少故工資上升，後竹供給增加故工資下降，所以工資差異縮小。另外，國中、高中程度中工作經驗屬於中間者與商職、專科、大學程度中工作經驗屬於兩端者工資差異縮小的主要因素，則為需求面之變動所致，而本文採用之需求變數為製造業多因素生產力指數，也因此發現台灣製造業的技術進步是屬於偏非技術性的技術進步，有利於低教育程度者，而不利於高教育程度者，故此項需求面因素縮小了高低教育程度間的工資差異。

In this thesis, we firstly present a low-cost plasma display panel (PDP) data dispatcher for image enhancement. By taking advantage of the proposed ADS method with 10 subfields and data reordering, our design can reduce 20% of the PDP dispatcher cost and resolve the ¡§dynamic false contour¡¨ problem. Secondly, a bipolar-valued inner product processor for associative memory neural networks is proposed to compute the inner product of two bipolar-valued vectors. Our analysis shows that the delay of inner product is reduced significantly from O(2n) to O(n). We also propose a 3-dimensional address decoding structure associated with a corresponding data cell encoding arrangement for P+implant ROMs such that the data words are encoded and stored in the ROMs in a natural pattern. Not only is the size of the entire decoder shrunk, the access time and power dissipation is also greatly reduced, which is very suitable to be utilized in implantable devices. Finally, we introduce a multi-parameter implantable neural interface micro-stimulator system, including the external control module, the protocol, and the SOC (system-on-chip) chip. The proposed system is expected to carry out the externally given commands to stimulate the corresponding neural trunks. On the other way around, it can sense and deliver the response of the neural trunks to an external monitoring device in the future.

Abstract The tremendous progress in all aspects of signal processing technology has naturally been accompanied by a corresponding development of arithmetic techniques to provide high-speed operations at reasonable complexity. In the past, many architectural design efforts have focused on maximizing performance for frequently executed simple arithmetic operations such as addition and multiplication while left other rarely used operations ignored. In this dissertation, we firstly propose two design approaches for 64-b carry-lookahead adders (CLA) using a two-phase clocking dynamic CMOS logic since fast adders are the key elements in many digital circuits. Secondly, we place emphasis on the inner product operation since it is one of the most frequently used mathematical operations in the computation of digital neural networks. A ratioed 3-2 compressor is also presented to resolve several physical design problems that are not fully considered or implemented in previous research works. Finally we propose several fast 64b/32b integer dividers because the integer division is unavoidable in many important signal-processing applications.

2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011), June 27-30, 2011, Grand Hyatt Taipei, Taipei, Taiwan

京都大学 / 新制・論文博士 / 博士(情報学) / 乙第13425号 / 論情博第96号 / 新制||情||131(附属図書館) / (主査)教授 神田 崇行, 教授 吉川 正俊, 教授 湊 真一, 阿部 正幸 / 学位規則第4条第2項該当 / Doctor of Informatics / Kyoto University / DFAM

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