The generalized Fermat type difference equations

Kai Liu,Lei Ma,Xiaoyang Zhai 대한수학회 2018 대한수학회보 Vol.55 No.6

This paper is to consider the generalized Fermat difference equations with different types which ever considered by Li \cite{li}, Ishizaki and Korhonen \cite{IK}, Zhang \cite{zhangjie} and Liu \cite{liuk4,11,1177,liu}, respectively. Some new observations and results on these equations will be given.

The Clinical Observation of Inflammation Theory for Depression: The Initiative of the Formosa Long COVID Multicenter Study (FOCuS)

Shu-Tsen Liu(Shu-Tsen Liu),Sheng-Che Lin(Sheng-Che Lin),Jane Pei-Chen Chang(Jane Pei-Chen Chang),Kai-Jie Yang(Kai-Jie Yang),Che-Sheng Chu(Che-Sheng Chu),Chia-Chun Yang(Chia-Chun Yang),Chih-Sung Liang( 대한정신약물학회 2023 CLINICAL PSYCHOPHARMACOLOGY AND NEUROSCIENCE Vol.21 No.1

There is growing evidence that the coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is associated with increased risks of psychiatric sequelae. Depression, anxiety, cognitive impairments, sleep disturbance, and fatigue during and after the acute phase of COVID-19 are prevalent, long-lasting, and exerting negative consequences on well-being and imposing a huge burden on healthcare systems and society. This current review presented timely updates of clinical research findings, particularly focusing on the pathogenetic mechanisms underlying the neuropsychiatric sequelae, and identified potential key targets for developing effective treatment strategies for long COVID. In addition, we introduced the Formosa Long COVID Multicenter Study (FOCuS), which aims to apply the inflammation theory to the pathogenesis and the psychosocial and nutrition treatments of post-COVID depression and anxiety.

A Dual Functional Ti-Ga Alloy: Inhibiting Biofilm Formation and Osteoclastogenesis Differentiation via Disturbing Iron Metabolism

Fupeng Li,Kai Huang,Jinbing Wang,Kai Yuan,Yiqi Yang,Yihao Liu,Xianhao Zhou,Keyu Kong,Tao Yang,Jian He,Chunjie Liu,Haiyong Ao,Fengxiang Liu,Qian Liu,Tingting Tang,Shengbing Yang 한국생체재료학회 2023 생체재료학회지 Vol.27 No.00

Background Although biomedical implants have been widely used in orthopedic treatments, two major clinical challenges remain to be solved, one is the bacterial infection resulting in biofilm formation, and the other is aseptic loosening during implantation due to over-activated osteoclastogenesis. These factors can cause many clinical issues and even lead to implant failure. Thus, it is necessary to endow implants with antibiofilm and aseptic looseningprevention properties, to facilitate the integration between implants and bone tissues for successful implantation. To achieve this goal, this study aimed to develop a biocompatible titanium alloy with antibiofilm and anti-aseptic loosening dual function by utilizing gallium (Ga) as a component. Methods A series of Ti-Ga alloys were prepared. We examined the Ga content, Ga distribution, hardness, tensile strength, biocompatibility, and anti-biofilm performance in vitro and in vivo. We also explored how Ga3+ ions inhibited the biofilm formation of Staphylococcus aureus (S. aureus) and Escherichia coli (E. coli) and osteoclast differentiation. Results The alloy exhibited outstanding antibiofilm properties against both S. aureus and E. coli in vitro and decent antibiofilm performance against S. aureus in vivo. The proteomics results demonstrated that Ga3+ ions could disturb the bacterial Fe metabolism of both S. aureus and E. coli, inhibiting bacterial biofilm formation. In addition, Ti-Ga alloys could inhibit receptor activator of nuclear factor-κB ligand (RANKL)-dependent osteoclast differentiation and function by targeting iron metabolism, then suppressing the activation of the NF-κB signaling pathway, thus, showing their potential to prevent aseptic loosening. Conclusion This study provides an advanced Ti-Ga alloy that can be used as a promising orthopedic implant raw material for various clinical scenarios. This work also revealed that iron metabolism is the common target of Ga3+ ions to inhibit biofilm formation and osteoclast differentiation.

SOME RESULTS RELATED TO COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS OF CERTAIN TYPES

Liu, Kai,Dong, Xianjing Korean Mathematical Society 2014 대한수학회보 Vol.51 No.5

In this paper, we consider the growth and existence of solutions of differential-difference equations of certain types. We also consider the differential-difference analogues of Br$\ddot{u}$ck conjecture and give a short proof on a theorem given by Li, Yang and Yi [18]. Our additional purpose is to explore the similarity or difference on some problems in differential, difference and differential-difference fields.

GENERALIZED YANG'S CONJECTURE ON THE PERIODICITY OF ENTIRE FUNCTIONS

Liu, Kai,Wei, Yuming,Yu, Peiyong Korean Mathematical Society 2020 대한수학회보 Vol.57 No.5

On the periodicity of transcendental entire functions, Yang's Conjecture is proposed in [6, 13]. In the paper, we mainly consider and obtain partial results on a general version of Yang's Conjecture, namely, if f(z)ⁿf^(k)(z) is a periodic function, then f(z) is also a periodic function. We also prove that if f(z)ⁿ+f^(k)(z) is a periodic function with additional assumptions, then f(z) is also a periodic function, where n, k are positive integers.

Stability Analysis of Discrete-Time Piecewise-Linear Systems: A Generating Function Approach

Kai Liu,Jianghai Hu,Yu Yao,Baoqing Yang,Xin Huo 제어·로봇·시스템학회 2014 International Journal of Control, Automation, and Vol.12 No.5

This paper studies the exponential stability of a class of discrete-time piecewise-linear systems (DPLS). Some basic properties of the proposed DPLS are established, which enables the generating function approach to be used for the system stability analysis. By introducing the generating functions of DPLS and showing their properties, a sufficient and necessary condition for the exponential stability of DPLS is derived. Furthermore, the maximum exponential growth rate of system trajectories can be obtained exactly by computing the radii of convergence of the generating functions. The algorithm for computing the generating functions is developed and two examples are given to demonstrate the proposed approach.

Case Study: Slope Stability Assessment Considering 3D Nonlinear Shear Strength

Kai Liu,Guocai Wang,Peng Yuan,Huijian Zhang 대한토목학회 2024 KSCE Journal of Civil Engineering Vol.28 No.1

In this paper, factor of safety (FOS) considering three-dimensional (3D) and nonlinear shear strength of geomaterials is formulated based on the modified spatial mobilized plane (MSMP) model. The MSMP model has the desirable features of considering 3D strength and the nonlinear shear behavior of soils, compared with the widely used Mohr-Coulomb (M-C) model. The MSMP model is developed from the spatial mobilized plane model by relating the internal friction angle to the mean effective stress within the framework of critical state soil mechanics. Based on the developed MSMP model and the geometric relationships in the mobilized effective normal-shear stress plane, the nonlinear 3D FOS is defined as the ratio of mobilized shear strength to shear stress. The developed nonlinear 3D FOS is applied to slope parametric and case studies. The parametric studies show significant differences between the nonlinear 3D FOS by the MSMP model and the traditional linear two-dimensional (2D) FOS by the M-C model. The case study shows that the MSMP model and nonlinear 3D FOS can better capture the developed failure slope zone than the M-C model and linear 2D FOS.

Douglas-Peucker-Based Accelerated Similarity Measures for Massive AIS Trajectories

Kai WANG,Ryan Wen LIU,Yan LI,Maohan LIANG,Yi LIU,Jianhua WU,Jingxian LIU 국제이네비해양경제학회 2017 International Journal of e-Navigation and Maritime Vol.8 No.1

With the rapid development of the global economy, transport safety and security have become the key issues in maritime transportation all over the world. In practical applications, the Automatic Identification System (AIS)-based measurement of similarities between different vessel trajectories plays an important role in improving maritime transportation, e.g., maritime navigation, maritime supervision and management. However, the received AIS datasets are usually composed of a large amount of redundant information which could significantly increase the computational complexity. To deal with this problem, a Douglas-Peucker (DP)-based calculation method is introduced in this paper to accurately compress the spatio-temporal AIS trajectories while preserving the main geometrical structures. Based on the compressed trajectories, it is able to accelerate the Dynamic Time Warping (DTW) algorithm for the measurement of similarities between different vessel trajectories. In particular, the combination of DP and DTW has the capacity of significantly reducing the computational cost and guaranteeing the accuracy of similarity measures. The experimental results have demonstrated the superior performance of the proposed method in terms of computational cost and accuracy of similarity measures.

Reading and Writing Our Own Stories: The Alternative Reading Group

Kai-ling LIU 이화여자대학교 아시아여성학센터 2002 Asian Journal of Women's Studies(AJWS) Vol.8 No.2

Since women are the primary participants in most reading groups in Taiwan, this research experiments with the use of women's personal narratives in one such group. Reading of ordinary women's personal narratives encourages women to reflect on their own lives and then write out their own life stories. Further, with the sense of community that this reading and writing generates, women may come to a better recognition of their own value. This group, comprising ten middle-aged women, held two-hour meetings once a week for twenty weeks. In the reading phase, the participants read 7 publications of women's personal narratives, which came in various forms such as letters, diaries, autobiographies, oral testimonies, and biographies. In the writing phase, the participants wrote their life stories, dwelling on themes of family, education, women and the body, the family-in-law, care-giving, appearance, and miscellany. This exercise led to three kinds of results. First, the reading of ordinary women's personal narratives introduced participants with the form and content of writing life stories. Then, the writing of their own life stories enabled the women participants to re-evaluate their past. Third, with the reading, writing, and group sharing, a collection of writing or what I call a 'community of narratives' was formed. This helped the participants recognize the differences amongst them and at the same time to value their own experience.

Memetic Two-echelon Vehicle Routing Optimization Based on Q Learning Theory and Differential Evolution Algorithm

Liu Dongdong,Liu Kai,Wang Feng,Han Bo,Zhao Zhengping,Tan Fuxiao,Niu Lei 보안공학연구지원센터 2016 International Journal of u- and e- Service, Scienc Vol.9 No.8

In allusion to such problems as low accuracy and long convergence time in traditional two-echelon vehicle routing optimization algorithm, a Memetic algorithm (QDEMA) based on Q learning theory and differential evolution is proposed in this article to solve above problems. Firstly, it is necessary to research the two-echelon vehicle routing optimization problem and adopt the optimal segmentation method to obtain the relatively reasonable distribution plan for the first-echelon SDVRP problem in order to accordingly determine the distribution quantity of the transfer stations; secondly, the second-echelon MDVRP distribution scheme is solved to obtain the total distance and the total number of the distribution vehicles for the two-echelon optimization problem; thirdly, in allusion to the solution of the second-echelon MDVRP distribution scheme, Q learning theory and the differential evaluation algorithm are adopted to design new Memetic algorithm in order to globally optimize MDVRP distribution scheme; finally, the simulation experiment is carried out to verify the algorithm effectiveness.