mapping theorem 中文意思是什麼
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The second section : under the conditions of nonlinear boundary controbility, we consider the initial boundary value problem of camassa - holm equations with dissipative. by using the contractive mapping fixed point theorem and a priori estimates, the existence of global smooth s olution, global attractor in h ~ ( 2 ), t ime p eriodic s olution or almost - periodic solution and the global exponential stability are proved
第二部分：在非線性控制邊界條件之下，對于帶耗散項的camassa ? holm方程的初邊值問題，用壓縮映射不動點原理及先驗估計方法，證明了整體光滑解的存在性、整體解的指數穩定性、 h ~ 2空間中整體吸引子的存在性以及時間周期解和殆時間周期解的存在性。 -
We reduce the cauchy problem of equations ( 8 ), ( 9 ) to an equivalent integral equations by the fundamental solution of a second order partial differential equation. then using the contraction mapping principle and the extension theorem of the solution we prove the existence and uniqueness of the global generalized solutions and the existence and uniqness of the global classical solution
先是通過一個二階偏微分方程的基本解，把imbq型方程組歸） ， p ）的初值問題轉化為等價的積分方程組，然後利用壓縮映射原理、解的延拓定理等證明了歸） ，問的初值問題的整體廣義解和整體古典解的存在唯一性 -
The second chapter sets forth the theorem basis of fractal image compression. by researching the property of iterate function system in metric space, two basic theorems are brought outthe fixed - point theorem of contract mapping and collage theorem. in the third chapter, fractal image compression method based on block partition is discussed and implemented
接著在第二章中闡述了分形圖象壓縮的理論基礎，通過對完備空間中迭代函數系統性質的研究，提出了分形圖象壓縮的兩個基本定理：壓縮映射的不動點定理和拼貼定理。 -
2. by doing precise computation of spectral radius of linear operator of linear equation and by using measure of noncompactness and leray - schauder type fixed point theorem of condensing mapping, the existence and the uniqueness of the solutions are obtained, which extend the results recently achieved in this field
二、通過線性方程解運算元譜半徑的論證，在緊型條件下利用凝聚映射的leray - schauder不動點定理及冪壓縮映射不動點定理，獲得了解的存在性與唯一性結果，這些結果推廣了近期這方面已有的一些結果。 -
This paper based on the definition of measurable mapping and the characters of mapping, gives the detailed identification of judging measurable mapping theorem
摘要根據可測映射的定義以及映射的相關性質，給出了關于判定可測映射的相關定理的詳細證明。 -
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。 -
At first, we introduce a class of generalized s - r - kkm type mapping in g - convex space, and establish generalized s - r - kkm type nonempty intersection theorem under the noncompact setting of g - convex space. as for application, some new minimax inequalities, saddle point theorem and existence theorem of maximal elements are proved in g - convex spaces ; second, by using the generalized r - kkm mapping and generalized r - kkm theorems in [ 13 ], some new existence theorem of maximal elements, existence theorem of equilibrium point for the abstract generalized vector equilibrium problem and existence theorem of solutions for equilibrium problem with lower and upper bounds are obtained in topological spaces
首先，我們在g -凸空間內引入了廣義s - r - kkm型映像，並在非緊設置下建立了一類新的廣義s - r - kkm型非空交定理，作為應用，證明了g -凸空間內一些新的極大極小不等式、鞍點定理和極大元存在定理；其次，利用文[ 13 ]中引入的廣義r - kkm映像和廣義r - kkm定理，在拓撲空間上得到了一些新的極大元存在定理、抽象廣義矢量平衡問題平衡點的存在定理和有上下界的平衡問題解的存在性定理。 -
The open mapping theorem and the closed graph theore
空間的開射定理及閉圖定理 -
The level - set method for open mapping theorem and closed graph theorem of menger spaces
空間的開射及閉圖定理 -
A mapping theorem on sn - metrizable spaces
可度量化空間的映射定理 -
To the first equation, the banach contraction mapping theorem is used to show the local existence of the solutions, we use potintial well method to prove the global existence and the decay rate of the solutions, to the blow - up of the solution we use the energy method
本文主要採用bananch壓縮映射原理來獲得解的局部存在性；採用勢井方法來獲得解的整體存在性和衰減估計；對解的爆破結論的證明主要採用能量方法；對解的能量衰減估計主要採用能量擾動方法。 -
In 1982, a weak convergence theorem for nonexpensive semigroups in uniformly convex banach space was first established by miyadera and kobaysi and it was generalized to that for commutative semigroup of asymptotically nonexpansive mappings by oka [ 15 ]. feathers and dotson [ 16 ] and bose [ 1 ] gave the weak convergence theorem of asymptotically nonexpansive mappings in a uniformly convex banach space with weak continuous duality mapping by using opial ' s lemma [ 17 ]
也正是由miyadera和kobayasi於1982年首次在一致凸banach空中給出了非擴張半群的弱收斂定理，隨后，由okaf15 ]把此弱收斂定理推廣到交換半群的漸近非擴張映照。 -
A fixed point theorem for contraction - mapping series on p - metric space
距離空間中壓縮映像序列的不動點定理 -
Therefore debreu won the nobel economics prize in 1983, debreu proved the walras compete competition equilibrium exist theorem by fixed - point theorem of set - valued mapping
Debreu也因此於1983年獲得了諾貝爾經濟學獎， debreu是利用集值分析的方法以集值映射的不動點定理為工具證明walras經濟均衡理論的。 -
A fixed point theorem on the weak expansion mapping
弱膨脹映射及其不動點定理 -
The major tasks include : ( 1 ) expand the schema theorem for ga. the schema theorem with binary coding advanced by professor holland is expanded to limited integer, letter, floating point numbers the number of which value is limited, and their hybrid coding. ( 2 ) put forward replacing by the excellent chromosome ga ( recga ), superiority colony first ga ( scfga ) and improve the ga ; ( 3 ) make probability convergence analysis of recga using the theory of markov chain, random process ; ( 4 ) make convergence analysis of scfga using the principle of contractive mapping in functional analysis theory ; ( 5 ) design the test programs ( cap ) to resolve np problems ( course arrangement ) with gas ; based on recga, modify the arithmetic and then conduct tests
主要有以下幾方面工作： （ 1 ）將二進制編碼遺傳演算法的模式定理擴展到由有限整數、字母或取值個數有限的浮點數編碼，或它們混合編碼的遺傳演算法范圍； （ 2 ）提出最佳個體替換策略遺傳演算法（ recga ） 、優勢群體優先策略遺傳演算法（ scfga ） ，對遺傳演算法進行改進； （ 3 ）使用隨機過程理論markov鏈對recga進行了收斂性分析； （ 4 ）使用泛函分析理論壓縮映射原理對scfga進行了收斂性分析； （ 5 ）使用遺傳演算法設計了解決np類問題（排課問題）的測試程序（ cap ） ，並根據recga對演算法進行改進並進行測試。 -
3. as for the existence of positive solutions, the cone theory and the fixed point index of condensing mapping are employed, and the results of the existence of positive solutions are obtained in the case of superlinear and sublinear. the conclusions extend and improve the existence theorem which lou ben - dong extablished in 1996 about the question of sturm - liouville of banach spaces
三、對于正解存在性問題，我們應用凝聚映射的不動點指數理論，分別在超線性與次線性情形下進行討論，獲得了一些正解存在的結果，主要結果推廣和改進了1996年louben - dong對banach空間sturm - liouville問題所建立的存在性定理。 -
On this basis, the error theorem is obtained which divides the hausdorff distance between the original image and reconstructed image into two control parts. the fixed point of each contraction mapping is introduced, the fixed - point image ( which is tiled by all the fixed points ) is selected as an initial image when decoding, and is proved to be a good estimation of the attractor of the ifs
在此基礎上，得到誤差定理，將原始圖像與迭代圖像間的hausdorff距離分為兩個控制項，並提出基於選擇初始圖像的分形圖像壓縮方法，引入不動點圖像，解碼時選擇不動點圖像為初始圖像，並證明不動點圖像是迭代函數系統的吸引子的一個較好的近似。 -
( 1 ) the paper has studied the contractive mapping genetic algorithm, which can be converged to a global optimal solution proved by fixed - point theorem of banach space. it remedies the shortage of standard genetic algorithm. furthermore, the paper discusses the genetic operation in the algorithm such as the coding, select, cross over and mutation etc. it will be help to the next work about fusion with the neural network
本文融合神經網路技術和遺傳演算法，對軌道交通引起的地面振動進行了正分析和反演，並利用計算機技術實現了地面振動的三維動畫模擬，這主要包括： （ 1 ）研究了壓縮映射遺傳演算法，利用banach空間的不動點定理證明了壓縮映射遺傳演算法可以收斂到全局最優值，彌補了標準遺傳演算法不能收斂至全局最優值的不足。
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