arXiv subjects

Jihua Ma

Publications and source records attributed to Jihua Ma.

4 recordsLinked to original sources

arXiv2022

Dimensions of certain sets of continued fractions with non-decreasing partial quotients

Let $[a_1(x),a_2(x),a_3(x),\cdots]$ be the continued fraction expansion of $x\in (0,1)$. This paper is concerned with certain sets of continued fractions with non-decreasing partial quotients. As a main result, we obtain the Hausdorff dimension of the set \[\left\{x\in(0,1): a_1(x)\leq a_2(x)\leq \cdots,\ \limsup\limits_{n\to\infty}\frac{\log a_n(x)}{ψ(n)}=1\right\}\] for any $ψ:\mathbb{N}\rightarrow\mathbb{R}^+$ satisfying $ψ(n)\to\infty$ as $n\to\infty$.

math.NT↗

arXiv2020

Some exceptional sets of Borel-Bernstein Theorem in continued fractions

Let $[a_1(x),a_2(x), a_3(x),\cdots]$ denote the continued fraction expansion of a real number $x \in [0,1)$. This paper is concerned with certain exceptional sets of the Borel-Bernstein Theorem on the growth rate of $\{a_n(x)\}_{n\geq1}$. As a main result, the Hausdorff dimension of the set \[ E_{\sup}(ψ)=\left\{x\in[0,1):\ \limsup\limits_{n\to\infty}\frac{\log a_n(x)}{ψ(n)}=1\right\} \] is determined, where $ψ:\mathbb{N}\rightarrow\mathbb{R}^+$ tends to infinity as $n\to\infty$.

math.NT↗

arXiv2018

Fourier decay rate of coin-tossing type measures

The Fourier decay rate of a coin-tossing type measure is investigated. Explicit estimation is given. Our method relies upon a classical result of Hartman and Kershner. As an application, we present a new example of a measure whose Fourier decay rate could be as slowly as we please, and for this measure almost every point is absolutely normal.

math.FA↗

arXiv2016

Surface terminations and layer-resolved spectroscopy in 122 iron pnictide superconductors

The surface terminations of 122-type alkaline earth metal iron pnictides AEFe2As2 (AE = Ca, Ba) are investigated with scanning tunneling microscopy/spectroscopy (STM/STS). Cleaving these crystals at a cryogenic temperature yields a large majority of terminations with atomically resolved square-root-two (rt2) or 1*2 lattice, as well as the very rare terminations with 1*1 symmetry. By means of lattice alignment and chemical marking, we identify these terminations as rt2-AE, 1*2-As, and rt2-Fe surfaces, respectively. Layer-resolved spectroscopy on these terminating surfaces reveals a well-defined superconducting gap on the As terminations, while the gap features become weaker and absent on AE and Fe terminations respectively. The local gap features are hardly affected by the surface reconstruction on As or AE surface, whereas a suppression of them along with the in-gap states can be induced by As vacancies. The emergence of two impurity resonance peaks at +-2 meV is consistent with the sign-reversal pairing symmetry. The definite identification of surface terminations and their spectroscopic signatures shall provide a more comprehensive understanding of the high-temperature superconductivity in multilayered iron pnictides.

cond-mat.supr-con↗