Question

有没有好心人把下段文字翻译成英文，谢谢！急！！！！！！

压缩映射是泛函分析中的重要概念。近年来，许多学者对压缩映射进行了深入的研究，取得了丰硕的成果。本文在已有文献的基础上对压缩映射的性质及在数列极限中的应用做了进一步的研究,首先对 压缩映象原理中所涉及到的相关定义进行了总结,其次给出与 压缩映象原理及其相关定理进行了详细的论述和证明,最后论述 压缩映象原理在极限中的应用。
不要用软件翻译

Answer 1

压缩映射是泛函分析中的重要概念。
Compression mapping is the important concept of functional analysis.

近年来，许多学者对压缩映射进行了深入的研究，取得了丰硕的成果。
In recent years, many scholars on compression mapping studied, have made great achievements.

本文在已有文献的基础上对压缩映射的性质及在数列极限中的应用做了进一步的研究,首先对 压缩映象原理中所涉及到的相关定义进行了总结,其次给出与 压缩映象原理及其相关定理进行了详细的论述和证明,最后论述 压缩映象原理在极限中的应用。
In this paper, on the basis of existing literature 1-set-contractive mapping properties and the application in sequence limit further research, at first principle of contractive mappings involved related definitions are summarized, then with the principle and contractive mappings related theorem are discussed in detail and proof, it finally discussed the principle of contractive mappings in the limit of application.

Answer 2

Contraction mapping is an important concept in functional analysis. In recent years, many scholars have conducted in-depth on the contraction mapping studies, and achieved fruitful results. In this paper, the literature on the contraction mapping on the basis of the nature and limits of series do further research, first mapping principle involved in the relevant definitions are summarized, followed by the give and mapping Principle and related theorems are discussed in detail and prove, finally discusses the mapping principle in the limit of the application.

Answer 3

Compression mapping is the important concept of functional analysis. In recent years, many scholars on compression mapping studied, have made great achievements. In this paper, on the basis of existing literature 1-set-contractive mapping properties and the application in sequence limit further research, at first principle of contractive mappings involved related definitions are summarized, then with the principle and contractive mappings related theorem are discussed in detail and proof, it finally discussed the principle of contractive mappings in the limit of application.

Answer 4

In this paper, two-dimensional chaotic map based on digital image watermarking algorithm, Chaos is random, like noise and extreme sensitivity to initial conditions and so on. After a two-dimensional chaotic map will be scrambled digital watermark signal embedded in the low frequency coefficients of wavelet domain to achieve a hidden digital watermark, security and stability; using Arnold transform two-dimensional chaotic map scrambling the watermark signal, not only enhance the security of watermark signal, while resistance to improve the visual image shear attacks.
This paper introduces the definition of the degree of scrambling scrambling after the images for quantitative analysis. Arnold transformation by analyzing the period and control parameters to achieve the best of digital image scrambling. The digital watermark signal scrambling the original watermark signal scattered correlation was cut in the attack error symbol can be scattered as far as possible, thus effectively improving the digital watermarking algorithm against cropping attack performance.
To improve the robustness of digital watermarking algorithm, the introduction of m sequence spread spectrum watermark signal, the paper selected as the wavelet transform domain watermark embedding embedded, the four watermarking algorithm programs, respectively, of its anti-JPEG compression, cropping, scaling, plus noise, and other attacks were tested, come up with a most robust digital watermarking algorithm.
Finally, the paper discusses digital watermarking technology research and development directions, proposed how to effectively resist the image rotation, of a complete synchronization of digital watermarking technology is the future, an important problem to be solved.

Keywords: digital watermarking, two-dimensional chaotic map, image scrambling, spreading
Paper Type: Applied Research

Answer 5

Contraction mapping is an important concept in functional analysis. Many scholars have conducted deepgoing studies in this field and have achieved plentiful and substantial results. This paper, on the basis of existing documents, conducts a further research with regard to the properties of contraction mapping and its application in the limit of number sequence. To begin with, it summarises the relevant concepts involved in the contractio mapping theory. Then, it goes on to give a detailed discourse and verification on contraction mapping and relevant theorem. Finally, it elaborates on its application in limits.