arbitrary interval
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2021 ◽  
Vol 19 ◽  
pp. 67
Author(s):  
V.A. Kofanov

We establish sharp estimates of the $L_q$-norms on any finite interval for the polynomials and splines and their derivatives with the help of local $L_p$-norms of these polynomials and splines.


2019 ◽  
Vol 20 (2) ◽  
pp. 719
Author(s):  
Osman Alagoz ◽  
Birol Gunduz ◽  
Sezgin Akbulut

Author(s):  
N. Kukharska

At the current stage of the development of information systems and technologies, global computer systems and multimedia tools, as never before, there is an urgent need to ensure the reliability, security of storage of digital data and their transmission through open channels of information communications. One of the most promising and popular approaches to solving this problem is based on the applying of computer steganography methods. The purpose of the article is systematizing information about methods of textual steganography, namely methods of arbitrary intervals, carrying out a comparative bandwidth analysis. Methods of research - methods of textual steganography: the method of double spaces between words, the method of changing the space code, the method of changing the number of spaces at the end of text strings, the method of changing the number of spaces between words aligned to the width of the text. Methods of arbitrary interval are used to hide the data in the free space in the text. They use intervals between sentences, spaces at the end of text strings, intervals between words in the text, including those, which are aligned in width, manipulate  symbols of spaces, which  have different ASCII codes. They are used to organize secret transmission of confidential information through open communication channels. In the article, on the basis of the software complexes developed in the environment of the computer algebra MathCAD, the steganographic transformations, which consistent with the algorithms of the methods, are sequentially tracked. The question of the bandwidth of the constructed steganosystems was considered. Bandwidth is the maximum amount of additional information that can be embedded in one element (symbol) of the text container. So, the bandwidth of the double-space method between words and the method of changing the space code in the case of the Ukrainian-language text container is 1.75%. The method of changing the number of spaces between aligned by the width of the text of the words has a lower bandwidth of 0.4%. The bandwidth of the method of changing the number of spaces at the end of the text strings depends on the difference between the number of symbols in the longest line and all other lines. The article also outlines the advantages and disadvantages of each method. Conclusions. The arbitrary interval methods are effective provided that the text is presented in ASCII format. In general, text files are "inconvenient" containers. They lack redundancy in comparison, for example, with graphic or audio files. For such arbitrary interval methods as a method of changing the space code, the method of changing the number of spaces at the end of the text strings is characterized by the fact that the hidden data can not be obtained from a hard copy of the text file. Despite the drawbacks, arbitrary interval methods have reason to be applied because of the prevalence of text file files. Users of computer networks are constantly exchanging text messages. This is a routine everyday action, so text files, even those, which contain hidden confidential information, should not cause unnecessary interest among outsiders.


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