affine function 中文意思是什麼
affine function
解釋
仿射函數-
The main contributions of the second part of this dissertation are focused on the cryptographic properties of logical functions over finite field, with the help of the properties of trace functions, and that of p - polynomials, as well as the permutation theory over finite field : the new definition of chrestenson linear spectrum is given and the relation between the new chrestenson linear spectrum and the chrestenson cyclic spectrum is presented, followed by the inverse formula of logical function over finite field ; the distribution for linear structures of the logical functions over finite field is discussed and the complete construction of logical functions taking on all vectors as linear structures is suggested, which leads to the conception of the extended affine functions over finite field, whose cryptographic properties is similar to that of the affine functions over field gf ( 2 ) and prime field fp ; the relationship between the degeneration of logical functions and the linear structures, the degeneration of logical functions and the support of chrestenson spectrum, as well as the relation between the nonlinearity and the linear structures are discussed ; using the relation of the logical functions over finite field and the vector logical functions over its prime field, we reveal the relationship between the perfect nonlinear functions over finite field and the vector generalized bent functions over its prime field ; the existence or not of the perfect nonlinear functions with any variables over any finite fields is offered, and some methods are proposed to construct the perfect nonlinear functions by using the balanced p - polynomials over finite field
重新定義了有限域上邏輯函數的chrestenson線性譜，考察了新定義的chrestenson線性譜和原來的chrestenson循環譜的關系，並利用一組對偶基給出了有限域上邏輯函數的反演公式；給出了有限域上隨機變量聯合分佈的分解式，並利用隨機變量聯合分佈的分解式對有限域上邏輯函數的密碼性質進行了研究；給出了有限域上邏輯函數與相應素域上向量邏輯函數的關系，探討了它們之間密碼性質的聯系，如平衡性，相關免疫性，擴散性，線性結構以及非線性度等；討論了有限域上邏輯函數各類線性結構之間的關系，並給出了任意點都是線性結構的邏輯函數的全部構造，由此引出了有限域上的「泛仿射函數」的概念；考察了有限域上邏輯函數的退化性與線性結構的關系、退化性與chrestenson譜支集的關系；給出了有限域邏輯函數非線性度的定義，利用有限域上邏輯函數的非線性度與相應素域上向量邏輯函數非線性度的關系，考察了有限域上邏輯函數的非線性度與線性結構的關系；利用有限域上邏輯函數與相信息工程大學博士學位論文應素域上向量邏輯函數的關系，揭示了有限域上的廣義bent函數與相應素域上的廣義bent函數的關系，以及有限域上的完全非線性函數與相應素域上向量廣義bent函數之間的關系;給出了任意有限域上任意。 -
Since sontag - type control based on control lyapunov function is an important control law in robust stabilization of affine systems, we point out that is a kind of variable structural control in essence. due to this recognition and the fact that control lyapunov functions are difficult to be constructed, we propose the concept of weak control lyapunov function and then prove the stabilizing property and the robustness of sontag - type control. using the way of proposing the control lyapunov function and the special structure of sontag - type control, we investigate the dissipassivation control of a kind of perturbed nonlinear systems
基於控制李雅普諾夫函數的sontag - type控制，是仿射系統魯棒鎮定研究中一種非常重要的控制律，通過研究我們發現，該控制律實質上是一種變結構控制；基於這一認識，也考慮到控制李雅普諾夫函數難于構造，我們抽象出弱控制李雅普諾夫函數概念，並證明了基於弱控制李雅普諾夫函數的sontag - type控制的鎮定作用和優化特性；借鑒控制李雅普諾夫函數的抽象方式以及sontag - type控制的特殊結構，探討了一類受擾系統的耗散化控制；探討了齊性度理論與控制李雅普諾夫函數相結合的鎮定設計問題。 -
Based on this characterization, we improve the theoretic result which is the foundation of lyapunov backstepping design. the problem that how to construct a control lyapunov function from a weak lyapunov function is a significant one, because the successful reconstruction implies that robust analysis and design can be probed in depth. for affine nonlinear systems, we present a sufficient reconstruction condition and interpretate the constructing procedure by typical examples
刻畫一類存在半正定弱李雅普諾夫函數的全局漸近穩定系統，並用所得結果改進了李雅普諾夫遞推設計的一個重要理論依據；如何由弱李雅普諾夫函數重構控制李雅普諾夫函數，是一個十分重要的問題，因為成功的重構意味著可以進行深入的魯棒分產摘要析與設計，針對仿射系統我們給出了可以重構的充分條件，並用典型例子說明了構造過程
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