A MEAN VALUE FUNCTION AND ITS COMPUTATIONAL FORMULA RELATED TO D. H. LEHMER'S PROBLEM

Wang, Tingting Korean Mathematical Society 2016 대한수학회보 Vol.53 No.2

Let p be an odd prime and c be a fixed integer with (c, p) = 1. For each integer a with $1{\leq}a{\leq}p-1$, it is clear that there exists one and only one b with $0{\leq}b{\leq}p-1$ such that $ab{\equiv}c$ mod p. Let N(c, p) denote the number of all solutions of the congruence equation $ab{\equiv}c$ mod p for $1{\leq}a$, $b{{\leq}}p-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b{\bar{b}}{\equiv}1$ mod p. The main purpose of this paper is using the mean value theorem of Dirichlet L-functions and the properties of Gauss sums to study the computational problem of one kind mean value function related to $E(c,p)=N(c,p)-{\frac{1}{2}}{\phi}(p)$, and give its an exact computational formula.

ON THE FOURTH POWER MEAN OF GENERALIZED TWO-TERM EXPONENTIAL SUMS

Wang, Tingting Korean Mathematical Society 2013 대한수학회보 Vol.50 No.1

In this paper, we use the elementary method and the theory of complex functions to study the computational problem of the fourth power mean of the generalized two-term exponential sums, and give two exact identities for them.

A mean value function and its computational formula related to D. H. Lehmer's problem

Tingting Wang 대한수학회 2016 대한수학회보 Vol.53 No.2

Let $p$ be an odd prime and $c$ be a fixed integer with $(c, p)=1$. For each integer $a$ with $1\le a \leq p-1$, it is clear that there exists one and only one $b$ with $0\leq b \leq p-1$ such that $ab \equiv c \bmod p$. Let $N(c, p)$ denote the number of all solutions of the congruence equation $ab \equiv c \bmod p$ for $1 \le a, b \leq p-1$ in which $a$ and $\overline{b}$ are of opposite parity, where $\overline{b}$ is defined by the congruence equation $b\overline{b}\equiv 1 \bmod p $. The main purpose of this paper is using the mean value theorem of Dirichlet $L$-functions and the properties of Gauss sums to study the computational problem of one kind mean value function related to $E(c, p)=N(c, p)-\frac{1}{2}\phi(p)$, and give its an exact computational formula.

Anaerobic Ammonium-Oxidizing Bacteria in Cow Manure Composting

( Tingting Wang ),( Lijun Cheng ),( Wenhao Zhang ),( Xiuhong Xu ),( Qingxin Meng ),( Xuewei Sun ),( Huajing Liu ),( Hongtao Li ),( Yu Sun ) 한국미생물생명공학회(구 한국산업미생물학회) 2017 Journal of microbiology and biotechnology Vol.27 No.7

Composting is widely used to transform waste into valuable agricultural organic fertilizer. Anaerobic ammonium-oxidizing (anammox) bacteria play an important role in the global nitrogen cycle, but their role in composting remains poorly understood. In the present study, the community structure, diversity, and abundance of anammox bacteria were analyzed using cloning and sequencing methods by targeting the 16S rRNA gene and the hydrazine oxidase gene (hzo) in samples isolated from compost produced from cow manure and rice straw. A total of 25 operational taxonomic units were classified based on 16S rRNA gene clone libraries, and 14 operational taxonomic units were classified based on hzo gene clone libraries. The phylogenetic tree analysis of the 16S rRNA gene and deduced HZO protein sequences from the corresponding encoding genes indicated that the majority of the obtained clones were related to the known anammox bacteria Candidatus “Brocadia,” Candidatus “Kuenenia,” and Candidatus “Scalindua.” The abundances of anammox bacteria were determined by quantitative PCR, and between 2.13 × 10⁵ and 1.15 × 10⁶ 16S rRNA gene copies per gram of compost were found. This study provides the first demonstration of the existence of anammox bacteria with limited diversity in cow manure composting.

The relationship between polymorphism of insulin-like growth factor I gene and susceptibility to type 2 diabetes in Uygur population, Xinjiang, China

Wang Tingting,Maimaitituersun Gulixiati,Shi Haonan,Chen Cheng,Ma Qi,Su Yinxia,Yao Hua,Zhu Jia 한국유전학회 2022 Genes & Genomics Vol.44 No.4

Background: Type 2 diabetes (T2DM) susceptibility varies among different populations and is affected by gene single nucleotide polymorphism (SNP). Insulin-like growth factor (IGF)-1 gene, which has many SNP loci, is involved in T2DM pathogenesis. However, the relationship of IGF-1 gene polymorphism with T2DM in Uyghur population is less studied. Objective: To investigate the relationship between T2DM susceptibility and polymorphism of IGF-1 gene in Uyghur population of Xinjiang, China. Methods: This study enrolled 220 cases (122 males (55.46%) and 98 females (44.54%); mean age of 53.40 ± 10.94 years) of T2DM patients (T2DM group) and 229 (124 males (54.15%) and 105 females (45.85%); mean age of 51.64 ± 10.48 years) healthy controls (control group). Biochemical indexes were determined. IGF-1 gene polymorphism was analyzed by SNP genotyping. Results: The levels of TG, HDL, LDL, BUN, and Cr were statistically significant between the T2DM group and the control group. In terms of IGF-1 polymorphism, T2DM group had higher frequency of AA genotype (OR = 2.40, 95% CI = 1.19-4.84) and allele A (OR = 1.55, 95% CI = 1.17-2.06) of rs35767 loci, suggesting that rs35767 is related to the occurrence of T2DM. A total of 5 gene interaction models was obtained through analyzing the interaction of 5 SNP loci with the GMDR method. Among them, the two-factor model that included rs35767 locus and rs5742694 locus had statistical difference with a large cross-validation consistency (10/10). The combination of GG/CC, GA/AA, AA/AA, and AA/AC genotype was in high-risk group, whereas the combination of GG/AA, GG/AC, GA/AC and GA/CC genotype was in the low-risk group. The risk of T2DM in the high-risk group was 2.165 times than that of the low-risk group (OR = 2.165, 95% CI = 1.478-3.171). Conclusion: TG, HDL, LDL, BUN, and Cr are influencing factors of T2DM in Uyghur population. The rs35767 locus of IGF-1 gene may be associated with T2DM in Uyghur population. The high-risk group composing of rs35767 locus and rs5742694 locus has a higher risk of T2DM.

Model-based Visual Servoing for Automatic Docking System of Circular Symmetrical Target with Large Displacement

Tingting Wang,Yuming Zhang,Bo Liu 제어·로봇·시스템학회 2023 International Journal of Control, Automation, and Vol.21 No.4

In this paper, a model-based visual servoing strategy with dual cameras is proposed for a circular symmetrical target with large displacement. The automatic docking system is composed of the fast-moving stage and the position-based visual servoing (PBVS) control stage, which enables a fast, accurate and stable docking task. A simplified stereo matching method is used in the fast-moving stage, and the CAD model-based tracking method with virtual visual servoing (VVS) method is applied in the PBVS control stage to estimate and update the current pose of the circular symmetrical docking target. Experiments of a robotic docking system validate the effectiveness, precision and flexibility of this strategy. The Root Mean Square errors of the docking results are less than 0.5 millimeters in translation and 0.1 degrees in rotation, and the average time for the whole docking task is no more than 1 minutes.

On the fourth power mean of generalized two-term exponential sums

Tingting Wang 대한수학회 2013 대한수학회보 Vol.50 No.1

In this paper, we use the elementary method and the theory of complex functions to study the computational problem of the fourth power mean of the generalized two-term exponential sums, and give two exact identities for them.

Analysis of Urban Rail DC Short Circuit Fault and Vehicle-Network Protection Coordination Based on Transient Characteristics

Wang Tingting,Sun Guobin,Cao Hu,Zhang Zhexu,Chen Jinheng 대한전기학회 2023 Journal of Electrical Engineering & Technology Vol.18 No.3

During the operation of urban rail transit system, if the vehicle traction system has short-circuit fault, the vehicle protection device will act and cut off the short-circuit current. Under some extreme short circuit conditions, the protection device of power supply system will also act, and the whole power supply section will be powered off. This is because the action setting values of vehicle protection device and power supply system protection device are designed respectively, and their matching and reliability need to be analyzed. Based on this, this paper first models the urban rail transit power supply system and vehicle traction system, then compares the calculated mathematical model with the simulation model to verify the accuracy of the simulation model. Finally, the short-circuit current waveforms under different short-circuit conditions are simulated, and the action sequence and protection range of protection devices are analyzed according to the simulation results. The research results are of great significance to the characteristic analysis of short-circuit fault, the selection of vehicle protection devices and the setting of protection parameters of power supply system.

Hybrid Atmospheric Compensation in Free-Space Optical Communication

Tingting Wang,Xiaohui Zhao 한국광학회 2016 Current Optics and Photonics Vol.20 No.1

Since the direct-gradient (DG) method uses the Shack-Hartmann wave front sensor (SH-WFS), basedon the phase-conjugation principle, for atmospheric compensation in free-space optical (FSO) communication,it cannot effectively correct high-order aberrations. While the stochastic parallel gradient descent (SPGD)can compensate the distorted wave front, it requires more calculations, which is sometimes undesirablefor an FSO system. A hybrid compensation (HC) method is proposed by properly using the DG methodand SPGD algorithm to improve the performance of FSO communication. Simulations show that thismethod can well compensate wave-front aberrations and upgrade the coupling efficiency with fewcomputations, preferable correction results, and rapid convergence rate.

A Novel AC/DC Converter Based on Stacked Boost Circuit and Dual-Mode LLC Circuit

Tingting Yao,Yueshi Guan,Fang Li,Yijie Wang,Wei Wang,Dianguo Xu 전력전자학회 2019 ICPE(ISPE)논문집 Vol.2019 No.5

In this paper, a AC/DC converter based on stacked Boost circuit and dual-mode LLC circuit is proposed. In the Power Factor Correction (PFC) part, two Boost circuits are stacked to reduce switch voltage stress, also sharing one inductor operating in Boundary Conduction Mode (BCM). In the DC/DC part, a dual-mode LLC circuit is adopted based on two stacked half-bridge structure. The input voltage of LLC resonant tank can double or halve by switching between two operating modes. Hence, the voltage gain of LLC converter can be modified without large operating frequency modulation range. The proposed AC/DC converter can be utilized in widely input voltage variation condition. A 50W prototype is proposed in the laboratory and the experimental results verify the feasibility of the proposed converter.