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A SYSTEM OF FIRST-ORDER IMPULSIVE FUZZY DIFFERENTIAL EQUATIONS
Heng-You Lan 영남수학회 2008 East Asian mathematical journal Vol.24 No.1
In this paper, we introduce a new system of first-order impulsive fuzzy differential equations. By using Banach fixed point theorem, we obtain some new existence and uniqueness theorems of solutions for this system of first-order impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.
Lan, Heng-You 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.25 No.1
In this work, by using Xu's inequality, Nalder's results, the notion of $(A,\;{\eta})-accretive$ mappings and the new resolvent operator technique associated with $(A,\;{\eta})-accretive$ mappings due to Lan et al., we study the existence of solutions for a new class of $(A,\;{\eta})-accretive$ variational inclusion problems with non-accretive set-valued mappings and the convergence of the iterative sequences generated by the algorithms in Banach spaces. Our results are new and extend, improve and unify the corresponding results in this field.
A SYSTEM OF FIRST-ORDER IMPULSIVE FUZZY DIFFERENTIAL EQUATIONS
Lan, Heng-You The Youngnam Mathematical Society Korea 2008 East Asian mathematical journal Vol.24 No.1
In this paper, we introduce a new system of first-order impulsive fuzzy differential equations. By using Banach fixed point theorem, we obtain some new existence and uniqueness theorems of solutions for this system of first-order impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.
Yun Yeo Wook,정성진,You Sun Jin,Lee Dong Kyu,Lee Kyu Yong,한상웅,Jee Heng Ok,김호중 대한의학회 2004 Journal of Korean medical science Vol.19 No.2
Arterial thrombosis is relatively rare compared with venous thrombosis in nephrotic syndrome. However, the assessment of its pathogenesis and risk factors in indi-vidual patient with nephrotic syndrome is necessary to allow appropriate prophylactic management because it is a potentially serious problem. Hereby, with review of the literature, we report a case of a 53 yr-old man with cerebral infarction associated with nephrotic syndrome due to focal segmental glomerulosclerosis during the course of treatments with diuretics and steroid. It reveals that the hypercoagulable state in nephrotic syndrome can be associated with cerebral infarction in adults. Pro-phylactic anticoagulants can be considered to reduce the risk of serious cerebral infarction in nephrotic patients with risk factors such as severe hypoalbuminemia and on diuretics or steroid treatment, even in young patients regardless of types of underlying glomerular diseases.
SOLUTIONS OF A CLASS OF COUPLED SYSTEMS OF FUZZY DELAY DIFFERENTIAL EQUATIONS
Yu-ting Wu,Heng-You Lan,Fan Zhang 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.3
The purpose of this paper is to introduce and study a class of coupled systems of fuzzy delay differential equations involving fuzzy initial values and fuzzy source functions of triangular type. We assume that these initial values and source functions are triangular fuzzy functions and define solutions of the coupled systems as a triangular fuzzy function matrix consisting of real functional matrices. The method of triangular fuzzy function, fractional steps and fuzzy terms separation are used to solve the problems. Furthermore, we prove existence and uniqueness of solution for the considered systems, and then a solution algorithm is proposed. Finally, we present an example to illustrate our main results and give some work that can be done later.
Yang Jia-xi,Gao Dan,Qi You-wei,Zhang Heng 한국화학공학회 2022 Korean Journal of Chemical Engineering Vol.39 No.8
Carbon dioxide (CO2) emitted by fossil energy combustion is related to the greenhouse effect. To furtherstudy the motion dynamics of CO2 bubbles in various solutions so as to better absorb them, a CO2 bubble experimentalplatform was built. The growth and motion of a single CO2 bubble were experimented in five concentrations ofNaOH, NaHCO3 solutions and five viscosity deionized waters, photographed with a high-speed camera and importedinto PyCharm for analysis. Based on this, four kinds of CO2 bubbles were experimentally studied. The results show thatthe viscosity leads to the increase of rising time; the maximum rise time is 0.518 s when the viscosity is 100 mPa·s, theaspect ratio of CO2 bubble in solution, there will be an “L” distribution, and the minimum rise time is close to risingafter the bubble is separated from the injector. NaHCO3 inhibits the reaction between NaOH solution and CO2, resultingin the cross-section ratio change decreasing. The concentration of NaOH solution most conducive to CO2absorption is 0.039 g/ml and 0.058 g/ml.
Koh, Renwei Eric,Sun, Cha Chee,Yap, Yee Ling,Cheang, Pei Ling,You, Ah Heng The Korean Electrochemical Society 2021 Journal of electrochemical science and technology Vol.12 No.2
In this study, Monte Carlo (MC) simulation is conducted with recurrence relation to study the effect of SiO<sub>2</sub> with different particle size and their roles in enhancing the ionic conductivity and lithium transference number of PMMA composite polymer electrolytes (CPEs). The MC simulated ionic conductivity is verified with the measurements from Electrochemical Impedance Spectroscopy (EIS). Then, the lithium transference number of CPEs is calculated using recurrence relation with the MC simulated current density and the reference transference number obtained. Incorporation of micron-size SiO<sub>2</sub> (≤10 ㎛) fillers into the mixture improves the ionic conductivity from 8.60×10<sup>-5</sup> S/cm to 2.35×10<sup>-4</sup> S/cm. The improvement is also observed on the lithium transference number, where it increases from 0.088 to 0.3757. Furthermore, the addition of nano-sized SiO<sub>2</sub> (≤12 nm) fillers further increases the ionic conductivity up towards 3.79×10<sup>-4</sup> S/cm and lithium transference number of 0.4105. The large effective surface area of SiO<sub>2</sub> fillers is responsible for the improvement in ionic conductivity and the transference number in PMMA composite polymer electrolytes.