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1	無趨勢PBIB設計的建構和最佳化性質 / Construction and Optimality of Trend-free Versions of PBIB Designs 黃建中, Hwang, Chien Chung Unknown Date (has links) 實驗設計中，我們假設在區塊中存在一趨勢效應(trend effect)。此趨勢效應影響觀察值，也影響我們對區塊效應(block effect)和處理效應(treatment effect)的估計。此種設計模式不同於一般的區塊設計模式，因此須將趨勢效應加人設計模式中。　　Bradley and Yeh (1980)研究和討論此種趨勢效應在區塊設計模式中之影響，並定義出無趨勢設計(trend-free design)。所謂無趨勢設計，乃是在區塊設計模式中，趨勢效應被抵消不影響處理效應之分析。Bradley and Yeh (1983)推導了一個線性無趨勢設計存在的必要條件是r(k+1)≡0(mod 2)其中k為區塊大小，r為處理出現的次數。　　Bradley and Yeh進一步預測任一滿足r(k+1)≡0(mod2)的區塊設計，經過在區塊中處理位置調整後，可變為一個線性無趨勢設計。本篇論文的主要目的乃是在探討給定一GD設計(group-divisibledesigns)，檢驗和推導此預測是否為真。 / Yeh and Bradley conjectured that every binary connected block design with blocks of size k and a constant replication numberr for each treatment can be converted to a linear trend-free design by permuting the positions of theatments within blocks if and only if r(k+1)≡0 (mod 2). Chai and Majumdar (1993) proved that any BIB design which satisfies r(k+1)≡0 (mod 2) is even can be converted to a linear trend-free design. In this thesis, we want to examine this conjecture is true or not for group-divisible designs (GD designs). 趨勢消除相異表法組合全體最佳化部份分枝不完全區塊設計 elimination of trend effect system of distinct representatives universal optimality PBIB design GD designs Block designs
2	Jensen Inequality, Muirhead Inequality and Majorization Inequality Chen, Bo-Yu 06 July 2010 (has links) Chapter 1 introduces Jensen Inequality and its geometric interpretation. Some useful criteria for checking the convexity of functions are discussed. Many applications in various fields are also included. Chapter 2 deals with Schur Inequality, which can easily solve some problems involved symmetric inequality in three variables. The relationship between Schur Inequality and the roots and the coefficients of a cubic equation is also investigated. Chapter 3 presents Muirhead Inequality which is derived from the concept of majorization. It generalizes the inequality of arithmetic and geometric means. The equivalence of majorization and Muirhead¡¦s condition is illustrated. Two useful tricks for applying Muirhead Inequality are provided. Chapter 4 handles Majorization Inequality which involves Majorization and Schur convexity, two of the most productive concepts in the theory of inequalities. Its applications in elementary symmetric functions, sample variance, entropy and birthday problem are considered. system of distinct representatives Three Chord Lemma Birkhoff Theorem convex function concave function convex hull double stochastic matrix Jensen Inequality Lorenz Curve Majorization Inequality majorization Muirhead Inequality Muirhead condition Schur concave function Schur Criterion Schur convex function Schur Inequality supporting line Supporting Line Inequality

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無趨勢PBIB設計的建構和最佳化性質 / Construction and Optimality of Trend-free Versions of PBIB Designs

Jensen Inequality, Muirhead Inequality and Majorization Inequality