HAUSDORFF DIMENSION OF THE SET CONCERNING WITH BOREL-BERNSTEIN THEORY IN L¨UROTH EXPANSIONS

Luming Shen 대한수학회 2017 대한수학회지 Vol.54 No.4

It is well known that every $x\in(0,1]$ can be expanded to an infinite L\"{u}roth series with the form of \[ x=\tfrac{1}{d_1(x)}+\cdots+\tfrac{1}{d_1(x)(d_1(x)-1)\cdots d_{n-1}(x)(d_{n-1}(x)-1)d_n(x)}+\cdots, \] where $d_n(x)\geq 2$ for all $n\geq 1$. In this paper, the set of points with some restrictions on the digits in L\"{u}roth series expansions are considered. Namely, the Hausdorff dimension of following the set $$ F_{\phi}=\{x\in (0,1]: d_n(x)\geq \phi(n), \ {\rm{i. \ o.}} \ n\} $$ is determined, where $\phi$ is an integer-valued function defined on $\mathbb{N}$, and $\phi(n)\to \infty$ as $n\to \infty$.

Low-delay Node-disjoint Multi-path Routing using Complementary Trees for Industrial Wireless Sensor Networks

( Luming Liu ),( Zhihao Ling ),( Yun Zuo ) 한국인터넷정보학회 2011 KSII Transactions on Internet and Information Syst Vol.5 No.11

Complementary trees are two spanning trees rooted at the sink node satisfying that any source node`s two paths to the sink node on the two trees are node-disjoint. Complementary trees routing strategy is a special node-disjoint multi-path routing approach. Several complementary trees routing algorithms have been proposed, in which path discovery methods based on depth first search (DFS) or Dijkstra`s algorithm are used to find a path for augmentation in each round of path augmentation step. In this paper, a novel path discovery method based on multi-tree-growing (MTG) is presented for the first time to our knowledge. Based on this path discovery method, a complementary trees routing algorithm is developed with objectives of low average path length on both spanning trees and low complexity. Measures are employed in our complementary trees routing algorithm to add a path with nodes near to the sink node in each round of path augmentation step. The simulation results demonstrate that our complementary trees routing algorithm can achieve low average path length on both spanning trees with low running time, suitable for wireless sensor networks in industrial scenarios.

Vitamin D Receptor Gene, Matrix Metalloproteinase 3 Polymorphisms and the Risk of Intervertebral Disc Degeneration Susceptibility: Meta-Analysis

Luming Nong,Yongjing Huang,Shujie Zhao,Nanwei Xu 대한척추외과학회 2016 Asian Spine Journal Vol.10 No.5

Several studies have evaluated the association between vitamin D receptor, matrix metalloproteinase 3 (MMP-3) polymorphisms and the risk of intervertebral disc degeneration susceptibility. The findings were inconsistent. This meta-analysis aimed to systematically assess the association between vitamin D receptor, MMP-3 polymorphisms and the risk of intervertebral disc degeneration susceptibility. A search of various databases was done covering all papers published until December 31th, 2014. Eight, 4, 3 studies were finally included that addressed the risk of intervertebral disc degeneration susceptibility and vitamin D receptor FokI (rs2228570), ApaI (rs7975232), and MMP-3 (rs731236) polymorphisms, respectively. FokI (f vs. F: summary odds ratio [OR], 1.13; 95% confidence interval [CI], 0.76–1.69; ff vs. FF: OR, 1.02; 95% CI, 0.59–1.77; ff vs. Ff/FF: OR, 1.05; 95% CI, 0.70–1.58), ApaI (a vs. A: OR, 0.73; 95% CI, 0.45–1.19; aa vs. AA: OR, 0.53; 95% CI, 0.22–1.25 p =0.14; aa vs. AA/Aa: OR, 0.69; 95% CI, 0.53–0.89) in the vitamin D receptor gene and MMP3 polymorphisms (5A vs. 6A: OR, 1.92; 95% CI, 0.77–4.80; 5A5A vs. 6A6A: OR, 2.17; 95% CI, 0.75–6.24; 5A5A vs. 5A6A/6A6A: OR, 1.58; 95% CI, 0.72–3.44) were not obviously associated with risk of intervertebral disc degeneration susceptibility. FokI, ApaI polymorphisms in the vitamin D receptor gene and MMP-3 polymorphism are not obvious risk factors for intervertebral disc degeneration susceptibility.

Molecular dynamics study of Al solute-dislocation interactions in Mg alloys

Shen, Luming Techno-Press 2013 Interaction and multiscale mechanics Vol.6 No.2

In this study, atomistic simulations are performed to study the effect of Al solute on the behaviour of edge dislocation in Mg alloys. After the dissociation of an Mg basal edge dislocation into two Shockley partials using molecular mechanics, the interaction between the dislocation and Al solute at different temperatures is studied using molecular dynamics. It appears from the simulations that the critical shear stress increases with the Al solute concentration. Comparing with the solute effect at T = 0 K, however, the critical shear stress at a finite temperature is lower since the kinetic energy of the atoms can help the dislocation conquer the energy barriers created by the Al atoms. The velocity of the edge dislocation decreases as the Al concentration increases when the external shear stress is relatively small regardless of temperature. The Al concentration effect on the dislocation velocity is not significant at very high shear stress level when the solute concentration is below 4.0 at%. Drag coefficient B increases with the Al concentration when the stress to temperature ratio is below 0.3 MPa/K, although the effect is more significant at low temperatures.

HAUSDORFF DIMENSION OF THE SET CONCERNING WITH BOREL-BERNSTEIN THEORY IN LÜROTH EXPANSIONS

Shen, Luming Korean Mathematical Society 2017 대한수학회지 Vol.54 No.4

It is well known that every $x{\in}(0,1]$ can be expanded to an infinite $L{\ddot{u}}roth$ series with the form of $$x={\frac{1}{d_1(x)}}+{\cdots}+{\frac{1}{d_1(x)(d_1(x)-1){\cdots}d_{n-1}(x)(d_{n-1}(x)-1)d_n(x)}}+{{\cdots}}$$, where $d_n(x){\geq}2$ for all $n{\geq}1$. In this paper, the set of points with some restrictions on the digits in $L{\ddot{u}}roth$ series expansions are considered. Namely, the Hausdorff dimension of following the set $$F_{\phi}=\{x{\in}(0,1]\;:\;d_n(x){\geq}{\phi}(n),\;i.o.n}$$ is determined, where ${\phi}$ is an integer-valued function defined on ${\mathbb{N}}$, and ${\phi}(n){\rightarrow}{\infty}$ as $n{\rightarrow}{\infty}$.

A NOTE ON CONTINUED FRACTIONS WITH SEQUENCES OF PARTIAL QUOTIENTS OVER THE FIELD OF FORMAL POWER SERIES

Xuehai Hu,Luming Shen 대한수학회 2012 대한수학회보 Vol.49 No.4

Let $\mathbb{F}_q$ be a finite field with q elements and $\mathbb{F}_q((X^{-1}))$ be the field of all formal Laurent series with coefficients lying in $\mathbb{F}_q$. This paper concerns with the size of the set of points $x{\in}\mathbb{F}_q((X^{-1}))$ with their partial quotients $A_n(x)$ both lying in a given subset $\mathbb{B}$ of polynomials in $\mathbb{F}_q[X]$ ($\mathbb{F}_q[X]$ denotes the ring of polynomials with coefficients in $\mathbb{F}_q$) and deg $A_n(x)$ tends to infinity at least with some given speed. Write $E_{\mathbb{B}}=\{x:A_n(x){\in}\mathbb{B},\;deg\;A_n(x){\rightarrow}{\infty}\;as\;n{\rightarrow}{\infty}\}$. It was shown in [8] that the Hausdorff dimension of $E_{\mathbb{B}}$ is inf{$s:{\sum}_{b{\in}\mathbb{B}}(q^{-2\;deg\;b})^s$ < ${\infty}$}. In this note, we will show that the above result is sharp. Moreover, we also attempt to give conditions under which the above dimensional formula still valid if we require the given speed of deg $A_n(x)$ tends to infinity.

Comparative analysis of the gut microbiota in distinct statin response patients in East China

Baoqing Sun,Luming Li,Xinfu Zhou 한국미생물학회 2018 The journal of microbiology Vol.56 No.12

Statin response shows great interindividual variations. Recently, emerging studies have shown that gut microbiota is linked to therapeutic responses to drugs, including statins. However, the association between the gut bacteria composition and statin response is still unclear. In this study, gut microbiota of 202 hyperlipidemic patients with statin sensitive (SS) response and statin resistant (SR) response in East China were investigated by high throughput sequencing to compare the gut bacteria composition and biodiversity in distinct statin response patients. Higher biodiversity was detected in Group SS than Group SR. Specifically, group SS showed significantly increased proportion of genera Lactobacillus (P = 0.001), Eubacterium (P = 0.004), Faecalibacterium (P = 0.005), and Bifidobacterium (P = 0.002) and decreased proportion of genus Clostridium (P = 0.001) compared to Group SR. The results indicated that higher gut biodiversity was associated with statin sensitive response. The increased genera Lactobacillus, Eubacterium, Faecalibacterium, Bifidobacterium, and decreased genus Clostridium in patient gut microbiota may predict patient's statin response, and hence may guide statin dosage adjustments.

HOW THE PARAMETER ε INFLUENCE THE GROWTH RATES OF THE PARTIAL QUOTIENTS IN GCFε EXPANSIONS

Ting Zhong,Luming Shen 대한수학회 2015 대한수학회지 Vol.52 No.3

For generalized continued fraction (GCF) with parameter ε(k), we consider the size of the set whose partial quotients increase rapidly, namely the set Eε(α) := {x ∈ 2 (0, 1] : kn+1(x) ≥ kn(x)α for all n ≥ 1}, where α > 1. We in [6] have obtained the Hausdorff dimension of Eε(α) when ε(k) is constant or ε(k) ~ kβ for any β ≥ 1. As its supplement, now we show that: dimH Eε(α) = {[수식] So the bigger the parameter function ε(kn) is, the larger the size of Eε(α) becomes.

Preservation and Utilization of Pear (Pyrus L.) Germplasm Resources in China

Yufen Cao,Fengzhi Liu,Luming Tian,Yuan Gao 한국원예학회 2008 한국원예학회 기타간행물 Vol.- No.-

Theoretical Research on the Time Delay and Corresponding Issues for the Novel Category of Internet of Things Control System

Yucheng Zhang,Guoyong Liu,Luming Tan 보안공학연구지원센터 2016 International Journal of Future Generation Communi Vol.9 No.10

In this paper, we theoretically and numerically analyze the time delay and corresponding issues for the novel category of Internet of things control system. At present, the Internet of things technology progress and mature, people also gradually combine control system and Internet connection and make them to give full play to their strengths. Internet of things has great innovation in goods intelligent network, and the general Internet of things in the motion control system has a great development space, the future of control system is applied to the large number of the wireless fieldbus and sensor networks. To overcome the severe issues of the IOT system denoted as the time delay, we conduct research from following perspectives. (1) The control system modelling and analysis. Compared in the actual control system in an event-driven clock driver has many advantages such as when the controller equipment or setting of event-driven actuators equipment. (2) The time delay analysis with mathematical modelling. Due to the signal delay, controller cannot receive timely feedback information of the object which will seriously affect the dynamic performance of the remote control system. Complex math model is proposed to deal with the issues. In the final part, we numerically simulation the proposed model and theory compared with other famous methods, the result indicates that the proposed method obtain better performance and feasibility.