КФУ. Карточка публикации. 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.

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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 представления

Статьи в зарубежных журналах и сборниках

Год публикации

2009

Авторы, сотрудники КФУ

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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https://repository.kpfu.ru/?p_id=51341

Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Лернер Эдуард Юльевич	ru_RU
dc.date.accessioned	2009-01-01T00:00:00Z	ru_RU
dc.date.available	2009-01-01T00:00:00Z	ru_RU
dc.date.issued	2009	ru_RU
dc.identifier.citation	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.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/?p_id=51341	ru_RU
dc.description.abstract	Functional Analysis and Other Mathematics	ru_RU
dc.description.abstract	Functional Analysis and Other Mathematics	ru_RU
dc.language.iso	ru	ru_RU
dc.publisher	Springer-Verlag	ru_RU
dc.title	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.	ru_RU
dc.type	Статьи в зарубежных журналах и сборниках	ru_RU