Ulomljeni deli korenov pozitivnih realnih števil

diplomsko delo

Jasmina Kamberović (Author), Daniel Eremita (Mentor)

Abstract

Diplomsko delo obravnava aritmetično funkcijo M_r (n), ki je definirana s predpisom M_r (n)=[1/{r^(1/n) } ]. Predstavljene so osnovne lastnosti funkcije M_r (n) in z njo povezani rezultati, ki jih je v članku On the Fractional Parts of Roots of Positive Real Numbers izpeljal Melvyn B. Nathanson. V prvem poglavju so izpeljane in dokazane ocene za eksponentne in logaritemske funkcije. Predstavljeni so tudi nekateri osnovni pojmi. V prvem razdelku drugega poglavja je definirana M_r (n). Podane so osnovne lastnosti funkcije M_r (n), ki so obravnavane v naslednjih razdelkih. V drugem razdelku drugega poglavja je obravnavano naraščanje, asimptotičnost in enoličnost funkcije M_r (n) V tretjem razdelku je obravnavana linearna periodičnost funkcije M_r (n), izračunane so eksplicitne vrednosti funkcije M_r (n) in definirana je funkcija razlike %f. V četrtem razdelku je izpeljan algoritem za računanje M_(e^%(k/t) ) (n).

Keywords

diplomska dela;realna števila;aritmetične funkcije;matematika;korenjenje;

Data

Language:	Slovenian
Year of publishing:	2015
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[J. Kamberović]
UDC:	511.11(043.2):511.14
COBISS:	21263624
Views:	904
Downloads:	85
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Fractional parts of roots of positive real numbers
Secondary abstract:	In this graduation thesis arithmetic function M_(r ) (n)=[1/{r^(1/n) } ] is studied. Basic properties and some other results concerning M_r (n) are discussed. In the first chapter estimates for the exponential and logarithmic functions are derived. Also some basic concepts are presented. In the first section of the second chapter the arithmetic function M_r (n) is defined and some of its basic properties are presented. In the second section the growth, asyptotics and uniqueness of the function M_r (n) are discussed. In the third section linear periodicity of the M_r (n) is discussed, explicit values of the M_r (n) are computed and the difference function %f is defined. In the fourth section an algorithm to compute M_(e^%(k/t) ) (n) is derived.
Secondary keywords:	integer part;fractional part;root;real number;arithmetic function;periodic arithmetic function;linearly periodic arihmetic function;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	X, 53 f.
ID:	8731190