lipschitz 中文意思是什麼

I love alvin lipschitz more than i can possibly say

我愛艾文萊布尼茲勝過言語所能形容

Second, we discuss composition operators on bloch space with closed range. by using a distortion theorem of bonk, minda and yanagihara about bloch functions, we obtain the sharp estimation of the lipschitz continuity of the dilation of bloch functions. then, we improve a theorem of ghatage, yan and zheng about composition operators on bloch space with closed range

其次研究了bloch空間上有閉值域的復合運算元，先利用bonk 、 minda和yanagihara關于bloch函數的一個偏差定理，得到bloch函數伸縮率的lipschitz連續性的精確估計式，用這個估計式改進了ghatage 、 yan和zheng關于bloch空間上關于有閉值域的復合運算元的一個定理。

Section 3 and section 4 are the main parts of the paper. by employing the directional derivative and generalized gradient in the broad sense, as defined in this paper, the first order necessary condition and the first order sufficient condition of the single - objective non - smooth programming where the objective function is d - regular weak lipschitz function and constrained functions are regular weak lipschitz functions

第三節和第四節是本文的主要章節，以本文定義的廣義方向導數和廣義梯度為分析工具，對目標函數為d正則弱l函數，約束函數為正則弱l函數的單目標非光滑規劃分別給出了一階必要條件和一階充分條件。

Let / be a function from rn to r. following the definitions of the generalized gradients proposed by clarke and xu yihong, respectively, we define the d - regular weak lipschitz function and propose a new generalized gradient as follows where d _ f ( x ; d ) is the directional derivative of / in the direction d at the point x, namely some properties are proposed

第二節引入基本定義和記號，在clarke和徐義紅提出的各自的廣義梯度的基礎上，定義了一類d正則弱l函數，且提出了一個新的廣義梯度。設f ： r ~ n r ，其廣義梯度為其中為f在處沿方向d的方向導數，即並給出了若干性質定理。

We show that near a hyperbolic set a c ~ ( 1 ) endomorphism has the lipschitz shadowing property, and a hyperbolic endomorphism has the inverse shadowing property with respect to a class of continuous methods. moreover, each of these shadowing properties is also " uniform " with respect to c ~ ( 1 ) perturbation

證明了c ~ 1自同態在其雙曲不變集附近具有lipschitz跟蹤性，當c ~ 1自同態為雙曲時，對一類連續method而言具有反跟蹤性，並且這兩種跟蹤性相對c ~ 1小擾動均具有一致性。

Lipschitz - operator algebras on non - compact metric space

空間上運算元代數的超自反性

Fast algorithms of both discrete and orthonormal wavelet and wavelet packet coefficient are diagrammatized to be introduced. daubechies wavelet is applied to help to discuss the application and test on signal filtering and noise reduction with the principle and threshold implementation ; the basic principle to pickup the fault characteristics is introduced mainly about the relations between the maximum module and signal saltation point and how to characterize the saltation point with lipschitz exponent

展示了離散正交小波變換的mallat快速演算法和小波包系數分解的快速演算法；重點應用daubeches小波探討了小波變換在信號濾波去噪中的應用和實驗，闡述了其基本原理和通過閾值化處理實現濾波的具體方法；探討了用小波變換進行故障特徵提取的原理，說明了小波變換模極大值和信號突變點之間的關系以及怎樣用李氏指數來表徵突變點的性質。

We first show that the solution operator s ( t ) is lipschitz continuous, then prove the discrete solution operator s _ ( * ) = 5 ( t _ ( * ) ) satisfy the squeezing property, finally, we get the existence of the exponential attractor m. whose fractal dimensionality is finite

第四章，研究ginzburg - landau方程在三維空間的指數吸引子的存在性。首先證明解運算元s （ t ）是lipschitz連續的，然後證明離散解運算元s _ * = s （ t _ * ）滿足擠壓性，從而得到指數吸引子m的存在性。

We define a type of hyperbolicity on the full measure invariant set which is given by the oseledec ' s multiplicative ergodic theorem and prove that the system has the lipschitz shadowing property on it

對于由oseledec乘法遍歷定理得到的滿測度（ fullmeasure ）不變集定義了雙曲性，並證明了系統在這個不變集上具有lipschitz跟蹤性。

Iterative process for certain nonlinear mappingswith lipschitz condition

條件的非線性映象的迭代過程

Relative to sde, the study for the solution of bsde under non - lipschitz condition is absence, especially when the uniqueness of the solution can not be guaranteed, the existence of minimal and maximal solution of bsde are not be studied

相對于正向隨機微分方程，非lipschitz條件下倒向隨機微分方程解的性質的研究尚不夠豐富，特別是條件不能保證方程解唯一時，倒向隨機微分方程最大最小解的存在性尚未見有成果。

In chapter two, under non - lipschitz condition, the existence and uniqueness of the solution of the second kind of bsde is researched, based on it, the stability of the solution is proved ; in chapter three, under non - lipschitz condition, the comparison theorem of the solution of the second kind of bsde is proved and using the monotone iterative technique, the existence of minimal and maximal solution is constructively proved ; in chapter four, on the base of above results, we get some results of the second kind of bsde which partly decouple with sde ( fbsde ), which include that the solution of the bsde is continuous in the initial value of sde and the application to optimal control and dynamic programming. at the end of this section, the character of the corresponding utility function has been discussed, e. g monotonicity, concavity and risk aversion ; in chapter 5, for the first land of bsde, using the monotone iterative technique, the existence of minimal and maximal solution is proved and other characters and applications to utility function are studied

首先，第二章在非lipschitz條件下，研究了第二類方程的解的存在唯一性問題，在此基礎上，又證明了解的穩定性；第三章在非lipschitz條件下，證明了第二類bsde解的比較定理，並在此基礎上，利用單調迭代的方法，構造性證明了最大、最小解的存在性；第四章在以上的一些理論基礎之上，得到了相應的與第二類倒向隨機微分方程耦合的正倒向隨機微分方程系統的一些結果，主要包括倒向隨機微分方程的解關于正向隨機微分方程的初值是具有連續性的，得到了最優控制和動態規劃的一些結果，在這一章的最後還討論了相應的效用函數的性質，如，效用函數的單調性、凹性以及風險規避性等;第五章，針對第一類倒向隨機微分方程，運用單調迭代方法，證明了最大和最小解的存在性，並研究了解的其它性質及在效用函數上的應用。

Motivated by an idea of [ 5 ], we secondly consider in this chapter the behaviour of u e bvh ( ) composed with a lipschitz function to characterize sbvh fuctions, hence, to make preparation for proving the compactness theorem in the next section

其次討論heisenberg群上有界變差函數與lipschitz函數的復合行為以刻畫特殊有界變差函數。再次，通過建立sbv _ h函數的判據，我們證明bv _ h空間和sbv _ h空間的緊性定理。

Convergence of generalized lipschitz generalized - accretive operator by ishikawa iteration sequences with errors and applications

迭代序列的收斂性及應用

Then, a kind of wnn based on single - scaling multidimensional wavelet frames and its matching pursuit algorithm is introduced. it is applied to approximate the nonlinear terms with lipschitz property of nonlinear systems to establish the adaptive state observer. the robust fault detection is realized by the observer, demonstrating the predominant performance of the wnn

然後利用一種基於單尺度小波框架的小波網路，逼近一類滿足lipschitz條件的非線性系統的非線性項，構造自適應狀態觀測器，實現了系統的魯棒故障檢測，同時採用徑向基神經網路進行殘差處理，實現了故障預報。

Approximate fixed point sequences for a finite family of lipschitz pseudocontractive maps

有限個李普希茲偽壓縮映射近迫點序列的收斂性

Approximate fixed point sequences and convergence theorems for lipschitz pseudocontractive mappings in banach spaces

偽壓縮映射的近似不動點序列及其收斂定理

In the second part ( chapter 3 ), we consider the lipschitz shadowing and the inverse shadowing for c ~ ( 1 ) endomorphisms

第二部分（第三章） ，對riemann流形上c ~ 1自同態的lipschitz跟蹤性和反跟蹤性進行了研究。

The approximation of the fixed points of lipschitz strongly pseudocontractive mappings in lp spaces

強偽壓縮映射的不動點的迭代逼近

Fixed - point iteration for uniform lipschitz asymptotically nonexpansive mapping of uniform convex banach space

一致李普希茲漸進非擴張映射的不動點迭代問題