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 Trends to equilibrium in collisional rarefied gas theory file 포항공과대학교 이동현
수학강연회 Towards Trustworthy Scientific Machine Learning: Theory, Algorithms, and Applications file KAIST 신연종
수학강연회 Toward bridging a connection between machine learning and applied mathematics file 성균관대학교 홍영준
수학강연회 Topology of configuration spaces on graphs file KAIST 고기형
수학강연회 Topology and number theory file Univ. College London/포항공대 김민형
수학강연회 Topological surgery through singularity in mean curvature flow file 고등과학원 최경수
특별강연 Topological Mapping of Point Cloud Data file Stanford University Gunnar E. Carlsson
수학강연회 Topological aspects in the theory of aperiodic solids and tiling spaces file Georgia Institute of Technology, School of Mathematics and School of Physics Jean V. Bellissard
수학강연회 Theory and applications of partial differential equations file 서울대 변순식
수학강연회 The significance of dimensions in mathematics file Kyoto Univ./서울대학교 Heisuke Hironaka
수학강연회 The Shape of Data file Stanford University Gunnar E. Carlsson
수학강연회 The process of mathematical modelling for complex and stochastic biological systems file KAIST 김재경
수학강연회 The phase retrieval problem file Hong Kong University of Science and Technology Yang Wang
수학강연회 The Mathematics of the Bose Gas and its Condensation file KAIST 이지운
수학강연회 The Lagrange and Markov Spectra of Pythagorean triples file 동국대학교 김동한
수학강연회 The classification of fusion categories and operator algebras file Kyoto University Masaki Izumi
수학강연회 Symplectic topology and mirror symmetry of partial flag manifolds file 부산대학교 수학과 김유식
수학강연회 Symplectic Geometry, Mirror symmetry and Holomorphic Curves file 연세대 수학과 홍한솔
수학강연회 Symmetry Breaking in Quasi-1D Coulomb Systems file 서강대학교 Paul Jung
수학강연회 Sums of squares in quadratic number rings file Univ. of Kentucky David Leep
Board Pagination Prev 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Next
/ 15