Application of Ground LiDAR for The Investigation of Outcrop Discontinuities and Estimation of Associated Engineering Characteristics

Reliable and direct information about rock slope materials and discontinuity parameters from field investigation are keys to engineering design, structure maintenance and soil/water conservation. Under the impact of global climate change and the surge in extreme weather events, rapid and accurate equipment or procedures for geological engineering surveys are necessary to harmonize engineering facilities with natural environment. This study utilizes 3D laser scanning technology (also known as ground LiDAR), which obtains the coordinates of surface geometry rapidly in point clouds, to survey two outcrops. Applying ground LiDAR in a geological survey, we compare the results with those provided by the International Society of Rock Mechanics, and analyze the slope stability. This study also discusses the applicability and limitations of ground LiDAR technology in discontinuity investigation and estimation of rock mass engineering characteristics. Suggested operating procedures for the use of ground LiDAR technology in outcrop surveys are provided accordingly. The results show that ground LiDAR technology reduces the in-situ operation time significantly, thus facilitating efficient discontinuity surveys and outcrop parameters evaluation. However, the quantities of office work and the accuracy of point clouds depend on the velocity and accuracy of ground LiDAR surveys. Therefore, inspection of survey results and output parameter, along with the application and operating specifications of geological surveys, including point cloud resolution, reasonable error of superimposition, inspection procedures and data analysis, still await further research.岩石工程道路邊坡經現地調查獲得可靠、直接的岩石材料種類與不連續面參數，為確保工程設計施工、設施營運維護及環境水土保持之關鍵資訊。在近年全球氣候變遷與極端氣候事件規模與頻率加大的衝擊下，迅速、精準的工程地質調查工具與作業方法，為落實工程設施與自然環境永續發展的不二法門。本研究利用三維雷射掃描技術 (又稱光達技術，|iDAR)，運用其可快速取得露頭表面幾何坐標描述點雲的特性，透過2處露頭現地地質調查，探討地面光達在工址地質調查之應用，並比較國際岩石力學學會建議工址現地調查作業方法所獲得的參數，分析評估邊坡的穩定特性，據以提出地面光達應用於露頭不連續面調查與岩體工程特性評估的適用性與限制，並提出地面光達應用於露頭調查的作業程序。研究結果顯示，地面光達技術可大幅縮減現地調查作業時間，為露頭不連續面調查與參數評估的新利器，由於室內分析工作量和點雲的精度決定了|iDAR應用於露頭不連續面調查的速度與精準度，未來針對調查成果與產出參數的檢核、在地質調查的應用與作業規範，包括點雲解析度、疊合容許誤差以及資料分析與檢核程序等，有待進一步深入研究

On Serre-Auslander-Buchsbaum Theorem

In this note, we give self-contained proofs of the following three theorems: Theorem A (Auslander-Buchsbaum formula) The depth of a Noetherian local ring A is equal to the sum of the depth and the projective dimension of a nitely generated A-module M with nite projective dimension. Theorem B (Serre theorem) A Noetherian local ring is regular if and only if its global dimension is nite. Theorem C A regular local ring is a unique factorization domain.Contents Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Abstract (in Chinese) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Abstract (in English) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 Introduction 5 2 Preliminary results 7 2.1 Prime Avoidance Lemma . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Nakayama Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Exact sequence and Localization . . . . . . . . . . . . . . . . . . . . . 8 2.4 Basic homology tool . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5 Exterior Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.6 Noetherian and Artinian . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.7 Primary Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . 10 3 Dimensions, Degrees, and Principal ideal Theorem 12 3.1 Artin-Rees Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2 Hilbert Funcition of a Graded Module . . . . . . . . . . . . . . . . . 13 3.3 Hilbert-Samuel Function over a Local Ring . . . . . . . . . . . . . . . 14 3.4 Principal Ideal Theorem . . . . . . . . . . . . . . . . . . . . . . . . . 17 4 Some Homological Algebra 18 4.1 The Functor Ext . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 The Functor Tor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.3 Projective and Injective Dimension . . . . . . . . . . . . . . . . . . . 20 4.4 Projective Dimension over a Local Ring . . . . . . . . . . . . . . . . . 24 4.5 Resolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5 Depth 30 5.1 Regular sequence and Depth . . . . . . . . . . . . . . . . . . . . . . . 30 5.2 Auslander-Buchsbaum formula . . . . . . . . . . . . . . . . . . . . . . 33 5.3 The Koszul complex . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 6 Regular local rings 37 6.1 Regular local rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 6.2 Serre Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 6.3 A regular local ring is UFD . . . . . . . . . . . . . . . . . . . . . . . 4

A study on Procedure and Officer’s Duty of Reclamation System of Qing Dynasty from Regulation —Focusing on Regulation of Ministry of Revenue

本論文欲從法規範之角度探討清代開墾制度之程序與官員責任。歷經明末清初之戰爭後，一切制度百廢待舉，在農業社會的中國農田不僅是人民溫飽之工具，亦是政府稅金收入的重要來源之一，因此在對整頓明末以來之荒田即至為重要。後隨社會安定，人口逐漸增多，原有之土地資源已無法承載高度成長之人口，此時土地發展重點轉向因新增人口壓力之舒緩。從極盛到凋零，清代後期又再度面臨因戰爭造成之土地荒廢，就這樣開墾制度環繞著整個清代，由其生至其死。例來對於開墾制度之研究多從歷史學的角度切入，研究素材多著重於地方志或實錄，其對於清代各地方之開墾有深入之研究。本論文欲從規範著手探討清代政府對於開墾制度之想像，不著重於特定地區之研究，而是利用法規範建構清代開墾之規範架構。 本論文選定乾隆四十六年之《欽定戶部則例》進行分析，乾隆四十六年版本之《欽定戶部則例》為《欽定戶部則例》有系統性之編纂成冊，對於清代前期至中期之開墾制度研究富具意義。戶部掌管天下錢糧，《欽定戶部則例》中所規定者俱為財政事。本論文從財政角度切入《欽定戶部則例》研 究開墾制度在清代國家財政的大框架下所處之地位，對於清代財政之重要性為何。並試圖建構清代開墾之程序，亦即清代政府如何透過這套程序將荒地發放給人民以使其安居樂業。同時政府透過人民開墾政府能增加其稅基，為鼓勵開墾，清代對於荒地開墾因狀況之不同給予不同之優惠，本論文亦將就規範中之租稅優惠進行體系性之分析。最後，本論文將從案例出發，以清代地方官員之責任為中心，探討清代開墾法規範之實際運作情形