perturbation theorem 中文意思是什麼
perturbation theorem
解釋
攝動定理- perturbation : n. 1. 慌張，動搖；混亂。2. 狼狽，不安，焦慮。3. 引起不安[混亂]的事物；引起動搖的原因。4. 【天文學】攝動；【物理學】微擾。adj. -al
- theorem : n. 1. （能證明的）一般原理，公理，定律，法則。2. 【數學】定理。
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In latter part of chapter three, some exciting properties of the revised lagrangian function discussed first, which leads to form a dual algorithm of cora or cot. convergence theorem proved by banach perturbation theorem, bertsekas implicit function theorem ii and by analyzing hesse matrix of revised largrangian function
另一類是構造相應的lagrange函數及其一種對偶演算法的迭代格式，討論了修正lagrange函數的性質，並藉助banach擾動定理及bertsekas第h隱函數定理，及對修正lagrange函數hesse陣分析，證明了該演算法的收斂性 -
The paper is concerned with periodic solutions to nonautonomous second order hamilton systems where, m : [ 0, t ] - s ( rn, rn ) is a continuous mapping in the space s ( rn, rn ) of symmetric real ( n x n ) - matrices, such that for some u > 0 and all ( t, z ) [ 0, t ] x rn, ( m ( t ) x, x ) > u | x | 2. a s ( rn, rn ), f : [ 0, t ] x rn r is continuous and f : [ 0, t ] xr r exists, is continuous and we study the existence of periodic solutions of the systems by using ekeland variational principle and the saddle points theorem. we suppose that the nonlinearity vf and potential f belongs to a class of unbounded functional. our work improves the existed results. we obtained the results of multiplicity of periodic solutions of the systems by using lusternik - schnirelman category theory and the generalized saddle points theorem, and the functional does not need the condition of constant definite. at last, we obtained the existence of infinity many distinct periodic solutions of the corresponding non - perturbation systems by using the symmetric mountain pass theorem
（ ? ， ? ）為r ~ n中內積， | ? |為對應范數。 f [ 0 ， t ] r ~ n r連續， ? f （ t ， x ）存在且連續， h l ~ 1 （ 0 ， t ； r ~ n ） 。利用ekeland變分原理和鞍點定理討論了該系統周期解的存在性，把非線性項和位勢函數放寬到一類無界函數，推廣了這方面工作的一些已有結果；利用廣義鞍點定理和lusternik - schnirelman疇數理論得到了該系統的多重周期解，取掉了泛函的常定要求；最後利用對稱山路定理得到沒有擾動時系統的無窮多周期解。 -
In this paper, we have proved that an anti - bounded c _ ( 0 ) - group in infinite - dimensional reflexive banach spaces is not exponentially stable under generating compact perturbation, and that a c _ ( 0 ) - isometric semigroup in infinite - dimensional hilbert spaces has the same property. so, we have extended and improved russell theorem
在本文中，我們分別證明了無限維自反banach空間中的反有界c _ 0 -群和無限維hilbert空間中的c _ 0 -等距半群在生成的緊擾動下一定不具指數穩定性，從而推廣和改進了russell定理。 -
Some fundamental methods in mathematical analysis are applied to prove the unique decomposition theorem : the distance between vector - valued pseudo almost periodic functions in metric spaces and almost periodic functions is an ergodic perturbation
應用數學分析中的基本方法證明了唯一分解定理，即距離空間中的向量值偽概周期函數和概周期函數之間的距離是一個遍歷擾動。
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