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Extra Form
강연자 김동한
소속 동국대
date 2016-10-27

We introduce and study a new complexity function in combinatorics on words, which takes into account the smallest return time of a factor of an infinite word. We characterize the eventually periodic words and the Sturmian words by means of this function. Then, we establish a new result on repetitions in Sturmian words and show that it is best possible. We deduce a lower bound for the irrationality exponent of real numbers whose sequence of b-ary digits is a Sturmian sequence over {0,1,…,b-1} and we prove that this lower bound is best possible. If the irrationality exponent of \xi is equal to 2 or slightly greater than 2, then the b-ary expansion of \xi cannot be `too simple', in a suitable sense. Our result applies, among other classical numbers, to badly approximable numbers, non-zero rational powers of e, and log(1+1/a), provided that the integer a is sufficiently large. It establishes an unexpected connection between the irrationality exponent of a real number and its b-ary expansion.


List of Articles
카테고리 제목 소속 강연자
수학강연회 Anomalous diffusions and fractional order differential equations file University of Washington Zhen-Qing Chen
수학강연회 Seeded Ising Model for Human Iris Templates and Secure Distributed Iris Recognition file 서울대학교 최형인
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수학강연회 An equivalent condition to Bohr's for Dirichlet series file 포항공대 최윤성
수학강연회 On the Schauder theory for elliptic PDEs file 연세대학교 김세익
수학강연회 <학부생을 위한 ɛ 강연> 서비스 진보의 관점에서 본 AI technology file 이스트소프트 대표 정상원
수학강연회 Seifert fiberings file University of Oklahoma 이경배
수학강연회 Mixing time of random processes file 서울대 서인석
수학강연회 Periodic orbits in symplectic geometry file 서울대 강정수
수학강연회 <학부생을 위한 ɛ 강연> 196884=196883+1 file 이화여대 김현규
수학강연회 Mathematical Models and Intervention Strategies for Emerging Infectious Diseases: MERS, Ebola and 2009 A/H1N1 Influenza file 건국대학교 교수, 현 산업응용수학회 회장 정은옥
수학강연회 Convex and non-convex optimization methods in image processing file Hong Kong Baptist University Michael Ng
수학강연회 Creation of concepts for prediction models and quantitative trading file Haafor 이승환
수학강연회 <학부생을 위한 ɛ 강연> Introduction to the incompressible Navier-Stokes equations file UNIST 배한택
수학강연회 An introduction to hyperplane arrangements file 서울대 이승진
수학강연회 What happens inside a black hole? file 고등과학원 오성진
수학강연회 <학부생을 위한 ε 강연> Variable-driven sociological research with data innovations file 연세대학교 강정한
수학강연회 Subword complexity, expansion of real numbers and irrationality exponents file 동국대 김동한
수학강연회 <학부생을 위한 ε 강연> 동형암호와 근사정수론 file 서울대 천정희
수학강연회 4-manifold topology and disk embedding file 포항공과대학교 차재춘
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