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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 Mixed type PDEs and compressible flow file POSTECH 배명진
Math Colloquia <학부생을 위한 ɛ 강연> Introduction to the incompressible Navier-Stokes equations file UNIST 배한택
Math Colloquia Essential dimension of simple algebras file KAIST 백상훈
Math Colloquia 1 is big enough to understand 3 file 카이스트 백형렬
Math Colloquia 학부생을 위한 강연: Introduction to partial differential equations file 서울대학교 변순식
Math Colloquia Theory and applications of partial differential equations file 서울대 변순식
Math Colloquia Variational Methods without Nondegeneracy file POSTECH 변재형
Math Colloquia W-algebras and related topics file 서울대학교 서의린
Math Colloquia Mixing time of random processes file 서울대 서인석
Math Colloquia <2020년도 젊은 과학자상 수상 기념강연> Metastability of stochastic systems file 서울대학교 서인석
Math Colloquia L-function: complex vs. p-adic file 충북대학교 선해상
Math Colloquia Quantitative residual non-vanishing of special values of various L-functions file UNIST 선해상
Math Colloquia 행렬함수 Permanent의 극소값 결정과 미해결 문제들 file 제주대학교/서울대학교 송석준
Math Colloquia 학부생을 위한 강연: Choi's orthogonal Latin Squares is at least 61 years earlier than Euler's file 연세대학교 송홍엽
Math Colloquia Existence of positive solutions for φ-Laplacian systems file 이용훈 수학강연회,특별강연,대중강연
Math Colloquia 학부생을 위한 ε 강연회: Sir Isaac Newton and scientific computing file 서울대학교 신동우
Math Colloquia Towards Trustworthy Scientific Machine Learning: Theory, Algorithms, and Applications file KAIST 신연종
Math Colloquia <학부생을 위한 ε 강연> 압축센싱과 행렬완성 file 서울대 심병효
Math Colloquia <학부생을 위한 ɛ 강연> A mathematical approach to xEV battery system file LG화학 안형준
Math Colloquia 학부생을 위한 강연회: 통신의 New Trend, 그리고 Big Data file KT 전무 양현미
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