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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.
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.
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.
Liu, Kai,Long, Xiangyun,Li, Bochuan,Xiao, Xiazi,Jiang, Chao Korean Nuclear Society 2021 Nuclear Engineering and Technology Vol.53 No.9
In this work, a new hardening model is proposed for the depth-dependent hardness of ion-irradiated polycrystals with obvious grain size effect. Dominant hardening mechanisms are addressed in the model, including the contribution of dislocations, irradiation-induced defects and grain boundaries. Two versions of the hardening model are compared, including the linear and square superposition models. A succinct parameter calibration method is modified to parametrize the models based on experimentally obtained hardness vs. indentation depth curves. It is noticed that both models can well characterize the experimental data of unirradiated polycrystals; whereas, the square superposition model performs better for ion-irradiated materials, therefore, the square superposition model is recommended. In addition, the new model separates the grain size effect from the dislocation hardening contribution, which makes the physical meaning of fitted parameters more rational when compared with existing hardness analysis models.
Exponential Stability Analysis of Planar Piecewise-Linear Systems: An Integral Function Approach
Kai Liu,Yu Yao,Baoqing Yang,Venkataramanan Balakrishnan,Yang Guo 제어·로봇·시스템학회 2012 International Journal of Control, Automation, and Vol.10 No.2
This paper studies the exponential stability of continuous-time planar piecewise-linear systems (PPLS). By introducing a novel conception of integral function of PPLS and showing its properties, a sufficient and necessary condition for the exponential stability is derived. Furthermore, the exponential growth rate of system trajectories can be obtained accurately by computing the convergence radius of integral function. The algorithm for computing the integral function is developed and two examples are given to demonstrate the proposed approach.
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.
Liu, Kai,Zhang, Hao,Ng, Joseph Kee-Yin,Xia, Yusheng,Feng, Liang,Lee, Victor C. S.,Son, Sang H. IEEE 2018 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS - Vol.14 No.3
<P>This work aims at proposing a transfer learning (TL)-based framework to enhance system scalability of fingerprint-based indoor localization by reducing offline training overhead without jeopardizing the localization accuracy. The basic principle is to reshape data distributions in the target domain based on the transferred knowledge from the source domains, so that those data belonging to the same cluster will be logically closer to each other, whereas others will be further apart from each other. Specifically, the TL-based framework consists of two parts, metric learning and metric transfer, which are used to learn the distance metrics from source domains and identify the most suitable metric for the target domain, respectively. Furthermore, this work implements a prototype of the fingerprint-based indoor localization system with the proposed TL-based framework embedded. Finally, extensive real-world experiments are conducted to demonstrate the effectiveness and the generality of the TL-based framework.</P>
Cooperative Data Scheduling in Hybrid Vehicular Ad Hoc Networks: VANET as a Software Defined Network
Liu, Kai,Ng, Joseph K. Y.,Lee, Victor C.S.,Son, Sang H.,Stojmenovic, Ivan Institute of Electrical and Electronics Engineers, 2016 IEEE/ACM transactions on networking Vol.24 No.3
<P>This paper presents the first study on scheduling for cooperative data dissemination in a hybrid infrastructure-to-vehicle (I2V) and vehicle-to-vehicle (V2V) communication environment. We formulate the novel problem of cooperative data scheduling (CDS). Each vehicle informs the road-side unit (RSU) the list of its current neighboring vehicles and the identifiers of the retrieved and newly requested data. The RSU then selects sender and receiver vehicles and corresponding data for V2V communication, while it simultaneously broadcasts a data item to vehicles that are instructed to tune into the I2V channel. The goal is to maximize the number of vehicles that retrieve their requested data. We prove that CDS is NP-hard by constructing a polynomial-time reduction from the Maximum Weighted Independent Set (MWIS) problem. Scheduling decisions are made by transforming CDS to MWIS and using a greedy method to approximately solve MWIS. We build a simulation model based on realistic traffic and communication characteristics and demonstrate the superiority and scalability of the proposed solution. The proposed model and solution, which are based on the centralized scheduler at the RSU, represent the first known vehicular ad hoc network (VANET) implementation of software defined network (SDN) concept.</P>