KFU. Card publication. 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.

Form of presentation

Articles in international journals and collections

Year of publication

2009

Authors, employees of KFU

Lerner Eduard Yulevich, author

Bibliographic description in the original language

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.

Annotation

Functional Analysis and Other Mathematics

Place of publication

Berlin / Heidelberg

The name of the journal

Functional Analysis and Other Mathematics

Publishing house

Springer-Verlag

URL

http://link.springer.com/journal/11853/2/2/page/1#page-1

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=51341&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Lerner Eduard Yulevich	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/eng/?p_id=51341&p_lang=2	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	Articles in international journals and collections	ru_RU