Казанский (Приволжский) федеральный университет, КФУ
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COMPLEXITY OF PRIME-DIMENSIONAL SEQUENCES OVER A FINITE FIELD / E.YU. LERNER // FUNCTIONAL ANALYSIS AND OTHER MATHEMATICS, 2009, VOL. 2, ISSUES 2-4, PP. 251-255. V. I. ARNOLD HAS RECENTLY DEFINED THE COMPLEXITY OF A SEQUENCE OF N ZEROS AND ONES WITH THE HELP OF THE OPERATOR OF FINITE DIFFERENCES. IN THIS PAPER WE DESCRIBE THE RESULTS OBTAINED FOR ALMOST MOST COMPLEX SEQUENCES OF ELEMENTS OF A FINITE FIELD, WHOSE DIMENSION N IS A PRIME NUMBER. WE PROVE THAT, WITH N→∞, THIS PROPERTY IS INHERENT IN ALMOST ALL SEQUENCES, WHILE THE VALUES OF MULTIPLICATIVE FUNCTIONS POSSESS THIS PROPERTY WITH ANY N DIFFERENT FROM THE CHARACTERISTIC OF THE FIELD. WE ALSO DESCRIBE THE PRIME VALUES OF THE PARAMETER N WHICH MAKE THE LOGARITHMIC FUNCTION ALMOST MOST COMPLEX. ALL THESE SEQUENCES REVEAL A STRONGER COMPLEXITY; ITS ALGEBRAIC SENSE IS QUITE CLEAR.
Форма представленияСтатьи в зарубежных журналах и сборниках
Год публикации2009
  • Лернер Эдуард Юльевич, автор
  • Библиографическое описание на языке оригинала Complexity of prime-dimensional sequences over a finite field / E.Yu. Lerner // Functional Analysis and Other Mathematics, 2009, vol. 2, Issues 2-4, pp. 251-255. V. I. Arnold has recently defined the complexity of a sequence of n zeros and ones with the help of the operator of finite differences. In this paper we describe the results obtained for almost most complex sequences of elements of a finite field, whose dimension n is a prime number. We prove that, with n→∞, this property is inherent in almost all sequences, while the values of multiplicative functions possess this property with any n different from the characteristic of the field. We also describe the prime values of the parameter n which make the logarithmic function almost most complex. All these sequences reveal a stronger complexity; its algebraic sense is quite clear.
    Аннотация Functional Analysis and Other Mathematics
    Место издания Berlin / Heidelberg
    Название журнала Functional Analysis and Other Mathematics
    Издательство Springer-Verlag
    URL http://link.springer.com/journal/11853/2/2/page/1#page-1
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