expansion數學的問題，透過圖書和論文來找解法和答案更準確安心。 我們找到下列懶人包和總整理

Casanova’s Lottery: The History of a Revolutionary Game of Chance

為了解決expansion數學的問題，作者 這樣論述：

The fascinating story of an important lottery that flourished in France from 1757 to 1836 and its role in transforming our understanding of the nature of risk. In the 1750s, at the urging of famed adventurer Giacomo Casanova, the French state began to embrace risk in adopting a new Loterie. The p

rize amounts paid varied, depending on the number of tickets bought and the amount of the bet, as determined by each individual bettor. The state could lose money on any individual Loterie drawing while being statistically guaranteed to come out on top in the long run. In adopting this framework, th

e French state took on risk in a way no other has, before or after. At each drawing the state was at risk of losing a large amount; what is more, that risk was precisely calculable, generally well understood, and yet taken on by the state with little more than a mathematical theory to protect it. S

tephen M. Stigler follows the Loterie from its curious inception through its hiatus during the French Revolution, its renewal and expansion in 1797, and finally to its suppression in 1836, examining throughout the wider question of how members of the public came to trust in new financial technologie

s and believe in their value. Drawing from an extensive collection of rare ephemera, Stigler pieces together the Loterie’s remarkable inner workings, as well as its implications for the nature of risk and the role of lotteries in social life over the period 1700-1950. Both a fun read and fodder for

many fields, Casanova’s Lottery shines new light on the conscious introduction of risk into the management of a nation-state and the rationality of playing unfair games.

expansion數學進入發燒排行的影片

批量分割與多目標平行機台彈性零工式生產排程之探討

為了解決expansion數學的問題，作者陳信維 這樣論述：

在現實製造環境中，通常都存在許多無法預期的突發狀況或變數，對於生產排程皆有重大的影響。排程涵蓋了許多資訊，需要同時考量才能達到想要的目標，排程規劃多半採用數學的運算或啟發式演算法，需要規劃出一套能結合現實生活中的限制與有限的資源的生產系統，讓在客戶要求的交期時間內生產出符合品質的產品。當今的製造生產從過去單一且大量的型態，改變為少量多樣的製造型態。由固定的生產數量轉變為接單式生產模式，零工式生產也就隨著需求型態不同製造生產型態的轉變而變得日益重要和重視。本研究以彈性零工式生產製造排程為基礎，納入非等效平行機器的考慮，允許批量分割作業，可同時讓作業在多部平行機器進行處理加工，進而減縮加工生產作

業完工時間。本研究為了考量更貼近於實際製造現場，讓生產製造現場機台能夠不間斷生產，研究中也將制定彈性訂單作業時間、途程以及非等效平行機台的加工效率，使同類加工時間的作業子批量能盡量接近。另外本研究也同時具備考慮排程績效多目標的指標，除了考量製造現場績效方面外，並將多目標因素納入因素考量中，建構程完整的多目標排程，以利用於實際生產製造多變且多樣化的需求競爭環境。依以上考慮，隨著規模範圍擴大的問題與複雜度程度的增加，本研究選擇以基因演算法為最佳化演算的基礎，建置能處理多目標因素的排程問題模組，期望能達到更貼近實際生產情況的排程。本研究將交期滿足與製距兩項指標，納入排程多目標考量。

Casanova’s Lottery: The History of a Revolutionary Game of Chance

為了解決expansion數學的問題，作者 這樣論述：

The fascinating story of an important lottery that flourished in France from 1757 to 1836 and its role in transforming our understanding of the nature of risk. In the 1750s, at the urging of famed adventurer Giacomo Casanova, the French state began to embrace risk in adopting a new Loterie. The p

rize amounts paid varied, depending on the number of tickets bought and the amount of the bet, as determined by each individual bettor. The state could lose money on any individual Loterie drawing while being statistically guaranteed to come out on top in the long run. In adopting this framework, th

e French state took on risk in a way no other has, before or after. At each drawing the state was at risk of losing a large amount; what is more, that risk was precisely calculable, generally well understood, and yet taken on by the state with little more than a mathematical theory to protect it. S

tephen M. Stigler follows the Loterie from its curious inception through its hiatus during the French Revolution, its renewal and expansion in 1797, and finally to its suppression in 1836, examining throughout the wider question of how members of the public came to trust in new financial technologie

s and believe in their value. Drawing from an extensive collection of rare ephemera, Stigler pieces together the Loterie’s remarkable inner workings, as well as its implications for the nature of risk and the role of lotteries in social life over the period 1700-1950. Both a fun read and fodder for

many fields, Casanova’s Lottery shines new light on the conscious introduction of risk into the management of a nation-state and the rationality of playing unfair games.

微型電網併聯多模組變流器智慧型控制策略研究

為了解決expansion數學的問題，作者楊艷 這樣論述：

逆變器是微型電網系統中的重要電力電子介面，可將分佈式發電系統與當地負載連接構成微型電網系統，或者與公共大電網連接實現併網運行。隨著分佈式能源發電規模的擴大，考慮電力電子開關的應力以及系統冗餘性能，通常將多個小容量逆變器模組併聯以建立大容量的微電網系統。此外，介面逆變器也通過併聯運行方式將微型電網系統中不同的分佈式能源接至公共連接點。研究智慧型控制方法以提高微型電網系統中併聯逆變器模組的控制性能及優化微型電網輸出電力品質，對於提高分佈式能源接入微型電網的滲透率顯得相對重要。為了提高微型電網孤島運行模式下併聯逆變器模組在不同負載及不同運行狀況下的動態性能及供電可靠性，本文設計基於主-從電流均衡控

制策略下的併聯逆變器模组自適應模糊類神經網路模擬滑動模式控制(Adaptive Fuzzy-Neural-Network-Imitating Sliding-Mode Control, AFNNISMC)，將併聯逆變器模组視為主體，構建完整的數學模型以保證其系統級的穩定性，並在此基礎上，首先設計全域滑動模式控制(Total Sliding-Mode Control, TSMC)和具有自適應觀測器的全域滑動模式控制架構。為了提高系統的強健性、克服傳統全域滑動模式控制對系統詳細動力學模型的依賴，及消除由全域滑動模式控制引起的控制抖動現象，本文使用四層模糊類神經網路(Fuzzy Neural Net

work, FNN)來模擬全域滑動模式控制律，根據里亞普諾夫穩定理論(Lyapunov Stability Theorem)和投影算法(Projection Algorithm)，利用模糊神經網路與全域滑動模式控制律之間的近似誤差，設計網路參數的線上自適應調整律，以保證網路參數的收斂性和控制系統的穩定性。因此，即使系統存在不確定性的情況下，也可以保證併聯逆變器模組輸出高品質的電能，以及併聯逆變器模組之間高精度電流均衡性能。此外，當單一逆變器從併聯系統斷開或重新接入時，所提出的 AFNNISMC 可以保證併聯系統的不斷電運行，從而提高微型電網系統的冗餘度和操作靈活性。進一步，藉由數值模擬和實驗結

果，驗證所提出自適應模糊神類經網路模擬滑動模式控制的可行性和有效性。此外，亦與傳統的適應性全域滑動模式控制(Adaptive TSMC, ATSMC)和比例積分控制(Proportional-Integral Control, PIC)架構進行性能比較，驗證所提出的自適應模糊類神經網路模擬滑動模式控制的優越性。考慮到固定結構的模糊神類經網路難以兼顧計算負擔及控制性能，本文進一步研究 一 種 自 組 織 結 構 模 糊 類 神 經 網 路 模 擬 滑 動 模 式 控 制 (Self-Constructing Fuzzy-Neural-Network-Imitating Sliding-Mode

Control, SFNNISMC)，用於執行主-從電流均衡控制策略下的微型電網併聯逆變器模組的併網電流跟蹤控制，所設計的模糊類神經網絡同時具有結構和參數自學習能力。本文所提出自組織結構模糊類神經網路(Self-Constructing Fuzzy Neural Network, SFNN)中，輸入層的初始節點由併網逆變器模組的數目決定，而隸屬函數層的規則由動態規則生成機制依據當前的暫態輸入從無到有自動生成。同時，本結構還引入了動態派翠(Petri)網路實現規則刪減機制，派翠網路使用於重新激活與新接入的從逆變器相對應的規則，只有被派翠網路激活的規則相關的網路參數才會被線上更新，而不是所有的網路

參數皆更新，從而減輕參數學習過程的計算負擔。此外，利用里亞普諾夫穩定理論和投影算法設計網路參數的線上學習律，保證網路參數及併網電流跟蹤誤差的收斂性。藉由數值模擬展示所提出的自組織結構模糊類神經網路模擬滑動模式控制在併聯逆變器模組不同運行狀況下規則演化的過程。本文亦利用兩個逆變器模組併聯的實驗平臺，亦與傳統的比例積分控制(PIC)、滑動模式控制(Sliding-Mode Control, SMC)及固定結構的自適應模糊神經網路模擬滑動模式控制(AFNNISMC)進行對比實驗，進一步驗證所提出的自組織結構模糊類神經網路模擬滑動模式控制方案的優越性。