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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 Regularity theory for non-autonomous elliptic equations in divergence form file 서강대학교 옥지훈
수학강연회 Regularity theory for nonlocal equations file 한양대학교 김민현
특별강연 Regularization by noise in nonlinear evolution equations file Dep. Math., Kyoto Univ. Yoshio Tsutsumi
수학강연회 Restriction theorems for real and complex curves file 포항공과대학교 박종국
수학강연회 Riemann-Hilbert correspondence for irregular holonomic D-modules file 서울대학교/RIMS Masaki Kashiwara
수학강연회 Role of Computational Mathematics and Image Processing in Magnetic Resonance Electrical Impedance Tomography (MREIT) file KAIST 이창옥
수학강연회 Root multiplicities of hyperbolic Kac-Moody algebras and Fourier coefficients of modular forms file Univ. of Connecticut 이규환
수학강연회 Satellite operators on knot concordance file 건국대학교 김태희
수학강연회 Seeded Ising Model for Human Iris Templates and Secure Distributed Iris Recognition file 서울대학교 최형인
수학강연회 Seifert fiberings file University of Oklahoma 이경배
수학강연회 Seoul ICM 2014 유치과정 개요 및 준비전략 file 포항공과대학교 박형주
수학강연회 Sheaf quantization of Hamiltonian isotopies and non-displacability problems file Kyoto Univ./서울대학교 Masaki Kashiwara
수학강연회 Solver friendly finite element methods file Oklahoma State Univ. 구자언
수학강연회 Space.Time.Noise file Meijo University Takeyuki Hida
수학강연회 Spectral Analysis for the Anomalous Localized Resonance by Plasmonic Structures file 인하대학교 강현배
수학강연회 Structural stability of meandering-hyperbolic group actions file 제주대학교 김성운
수학강연회 Structures of Formal Proofs file 경북대학교 정주희
특별강연 Structures on Persistence Barcodes and Generalized Persistence file Stanford University Gunnar E. Carlsson
수학강연회 Study stochastic biochemical systems via their underlying network structures file 포항공과대학교 김진수
수학강연회 Subgroups of Mapping Class Groups file 서울대학교 김상현
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