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Extra Form
Lecturer 김동한
Dept. 동국대
date Oct 27, 2016

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
Category Subject Dept. Lecturer
Math Colloquia <학부생을 위한 ε 강연> 수학과 예술 - 초기 컴퓨터 그래픽 file 동양대학교 진중권
Math Colloquia The Lagrange and Markov Spectra of Pythagorean triples file 동국대학교 김동한
Math Colloquia Subword complexity, expansion of real numbers and irrationality exponents file 동국대 김동한
Math Colloquia Conformal field theory and noncommutative geometry file 동경대학교 Kawahigashi
Math Colloquia 돈은 어떻게 우리 삶에 돈며들었는가? (불확실성 시대에 부는 선형적으로 증가하는가?) file 농협은행 홍순옥
Math Colloquia Codimension Three Conjecture file 교토대학교/서울대학교 Masaki Kashiwara
Math Colloquia A brief introduction to stochastic models, stochastic integrals and stochastic PDEs file 고려대학교 김경훈
Math Colloquia What happens inside a black hole? file 고등과학원 오성진
Math Colloquia Conformal field theory in mathematics file 고등과학원 강남규
Math Colloquia On circle diffeomorphism groups file 고등과학원 김상현
Math Colloquia Topological surgery through singularity in mean curvature flow file 고등과학원 최경수
Math Colloquia <학부생을 위한 ɛ 강연> 양자상태의 기하학 file 고등과학원 김영훈
Math Colloquia Free boundary problems arising from mathematical finance file 경희대학교 전준기
Math Colloquia Structures of Formal Proofs file 경북대학교 정주희
Math Colloquia High dimensional nonlinear dynamics file 경북대학교 도영해
Math Colloquia Mathematical Models and Intervention Strategies for Emerging Infectious Diseases: MERS, Ebola and 2009 A/H1N1 Influenza file 건국대학교 교수, 현 산업응용수학회 회장 정은옥
Math Colloquia 원의 유리매개화에 관련된 수학 file 건국대학교 최인송
Math Colloquia Satellite operators on knot concordance file 건국대학교 김태희
Math Colloquia 학부생을 위한 ε 강연회: Constructions by ruler and compass together with a conic file 건국대/서울대 최인송
Math Colloquia Random walks in spaces of negative curvature file Yale Univ. Giulio Tiozzo
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