臺灣博碩士論文加值系統

由於X射線的相位問題，無法以傅立葉反轉換求得電子密度，分子的晶體結構便無法求解。目前已有許多方法可以克服此一問題，如直接法(Direct Method)、重原子法(Heavy Atom)、模擬退火法(Simulated Annealing)。但是對於巨大分子，我們仍面臨了驚人的計算量的極大挑戰。因此，我們提出以碎波來解析電子密度，希望利用碎波多層解析(multiresolution)的性質，能減少模擬退火法的計算量。

On account of “the X-ray Phase Problem”, it’s impossible to get the electronic density by inverse Fourier transformation(IFT). And the crystal structure of molecule can’t be solved by IFT. There are many methods to overcome the problem, such as Direct Method, Heavy Atom, and Simulated Annealing. But for macro-molecules, we still face a great challenge due to tremendous computing load. We propose a method by using wavelets to resolve the electronic density. We hope the multiresolution nature of wavelets can reduce the computing load for simulated annealing method.

第一章簡介 1-1
第二章模擬退火法
2-1　退火 2-1
2-2　模擬退火法 2-2
2-2-1 Metropolis算法 2-3
2-2-2　模擬退火法的內涵 2-4
第三章碎波
3-1　碎波初探 3-1
3-1-1　階梯函數 3-1
3-1-2　函數的平移與脹縮 3-2
3-1-3　多層解析空間 3-3
3-2　正交碎波理論 3-5
3-2-1　尺度函數與碎波函數 3-5
3-2-2　碎波的傅立葉轉換 3-6
第四章以碎波與模擬退火法求解晶體結構
4-1　X射線繞射相位問題 4-1
4-2　以碎波解決相位問題 4-2
4-2-1　基礎碎波應用 4-2
4-2-2　考慮函數的平移與脹縮 4-3
4-2-3　以碎波表示電子密度 4-4
4-3　以模擬退火法求解晶體結構 4-5
4-3-1　建立問題模型 4-5
4-3-2　擬定降溫程序 4-8
4-3-3　進行模擬退火法的運作 4-10
第五章程式介紹
5-1　系統資料設定 5-1
5-2　設定起始環境及定義外在變數 5-1
附錄
附錄一　程式主體　　　　　　　　　　　　　　附錄1-1
附錄二　程式設定檔　　　　　　　　　　　　　附錄2-1
附錄三　程式中其餘的函式　　　　　　　　　　附錄3-1
附錄四　X射線繞射資料 附錄4-1

第一章【1-1】E.L.Lawler, “The Traveling salesman problem : a guided tour of combinatorial optimization”, Wiley, New York , 1985.【1-2】Wu-Pei Su, “Simulated Annealing as a Tool for Ab Initio Phasing in X-ray Crystallography”, Acta Cryst, A51, 845(1995).【1-3】Yan-Song Chen, W. P. Su, Siva P. Mallela and Russell A. Geanangel, “Solution of a New Molecular Structure ((SnClGe(SiC3H9)3)4) by Simulated Annealing”, Acta Cryst, A53, 397(1997).第二章【2-1】S. Kirkpatrick, C.D. Gelatt Jr., and M.P. Vecchi, “Optimization by Simulated Annealing”, Science 220, 671(1983).【2-2】N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, J. Chem. Phys. 21, 1087(1953).【2-3】Shyanglin Lee, “Optimization with Simulated Annealing Algorithm”, Mingchi Institute of Technology Journal Vol. 25, 153 (1993).【2-4】方崇仰, “以基因法改良研究分子結構的退火法”, 2000.第三章【3-1】Ingrid Daubechies, “Ten Lectures on Wavelets”, SIAM, Philadelphia, Pennsylvania, 1992.【3-2】Howard L. Resnikoff, Raymond O. Wells, “Wavelet Analysis”, Springer-Verlag, New York, 1998.【3-3】單維彰, “First concept of wavelets”, 全華科技圖書, 台北, 1998.第四章【4-1】Charles Kittel, “Introduction to Solid State Physics”, John Wiley & Sons, Singapore, 1986.【4-1】John M. Cowley, “Diffraction Physics”, Elsevier Science, Netherlands, 1995.第五章【5-1】王仁宗私下提供