entropy inequality 中文意思是什麼

entropy inequality 解釋
熵不等式
  • entropy : n. 1. 【物理學】熵。2. 【無線電】平均信息量。
  • inequality : n. 1. 不平等，不平均，不平衡，不等量。2. 不相同，互異。3. 變動，變化，高低，起伏。4. 【數學】不等式；【天文學】均差。5. （平面等的）不平坦。6. 不勝任。
  1. In the fields of fluid dynamics, entropy inequality reflects the second law of thermodynamics. i. e. entropy must increase across shock waves ( a kind of discontinuity ). all kind of approximate schemes should reflect the fact that it must satisfies some kind of discrete entropy inequality ). from the view of practical computation, stability and theo - retical error of any kind discrete schemes all dependend of the smoothness of the solution of ( 0. 2. 1 ). generally, the approximate solution have good stability and theoretial error in the area where the solutions have more regularity and poor stability and theoretial error in other area

    從流體力學來看，它事實上是熱力學第二定理的反映，即熵越過激波（一種間斷）要增加。各種估計格式構造的估計解應反映這一事實，即滿足熵不等式。從實際計算來看，總是通過離散化求解，不考慮計算的積累誤差，它的穩定性與計算精度都依賴與真解的光滑性，一般說，在解較光滑的區域有較好的穩定性與計算精度，而在較粗糙的區域則相反。
  2. The applications of shannon entropy and kullback ' s cross - entropy as perturbations are discussed. by maximizing the perturbed lagrangians in dual space, we obtain the exponential penalty function and exponential multiplier penalty function, respectively, for inequality constrained nlps

    文中分別以shannon熵函數和kullback叉熵函數作為攝動函數，導出其對偶函數分別是原問題的指數罰函數和指數乘子罰函數。
  3. Due to the poor regularity of solutions at large time. ( 0. 2. 1 ) can not defined in classical way. i, e., the defi nition of the derivatives at any points has no sense. so it may be rather difficult in the research of classical way and must be defined in weak sense. in order to guarantee the uniqueness of weak solutions, a condition ( entropy inequality ) must be need to pick out " good " solution ( entropy solutions )

    由於大時間范圍內守恆律（ 0 . 1 . 1 ）的解表現為很差的正則性，它不能在古典意義下定義，即在每一點下的導數無意義，使得古典辦法研究遇到很大困難，它只能在弱意義下定義弱解，但往往這種弱解不唯一，需要某條件限制確保解的唯一性，在數學上稱為熵條件，滿足該條件的弱解稱為熵解。
  4. The second chapter reveals the mathematical essence of entropy regularization method for the finite min - max problem, through exploring the relationship between entropy regularization method and exponential penalty function method. the third chapter extends maximum entropy method to a general inequality constrained optimization problem and establishes the lagrangian regularization approach. the fourth chapter presents a unified framework for constructing penalty functions by virtue of the lagrangian regularization approach, and illustrates it by some specific penalty and barrier function examples

    第一章為緒論，簡單描述了熵正則化方法與罰函數法的研究現狀；第二章，針對有限極大極小問題，通過研究熵正則化方法與指數（乘子）罰函數方法之間的關系，揭示熵正則方法的數學本質；第三章將極大熵方法推廣到一般不等式約束優化問題上，建立了拉格朗日正則化方法；第四章利用第三章建立的拉格朗日正則化方法，給出一種構造罰函數的統一框架，並通過具體的罰和障礙函數例子加以說明。
  5. In this thesis, we extend the entropy regularization method in two ways : from the min - max problem to general inequality constrained optimization problems and from the entropy function to more general functions

    本文從兩個方面發展了這種熵正則化方法，即將其從極大極小問題推廣到一般不等式約束優化問題上和用一般函數代替熵函數作正則項，建立新的正則化方法。
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