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Tuning of BixOyCl formation with sonication time during ultrasound-hydrothermal preparation
Zeqing Long,Guangming Zhang,Ting Wei,Lijun Niu,Jia Zhu,Jinwei Li 한국공업화학회 2020 Journal of Industrial and Engineering Chemistry Vol.84 No.-
Developing novel and visible-light drive photocatalysts is a hot topic, and bismuth oxychloride is one ofthe popular photocatalysts. In this paper, a series of bismuth oxychloride were synthesized by ultrasonic-hydrothermal method with different ultrasonic time. By simply changing the ultrasonic time, we cancontrol the morphology, structure, stoichiometry and photoelectric performance of bismuth oxychloride. The possible mechanism for the formation of BixOyCl photocatalysts involved the ultrasonic destructionof chemical bonds and increase of oxygen vacancy concentration, and the influence of ultrasonic on thepH during preparation. The sample of ultrasonic 30 min (U-30) showed the best photocatalytic activitydue to the suitable morphology, structure, photoelectric performance, the formation of theheterostructure, and the presence of oxygen vacancies. For the removal of Rhodamine B (/Ciprofloxacin),the reaction rate constant for U-30 was 10.4 (/3.6), 4.9 (/1.6), 6.9 (/4.8), and 9.3 (/2.3) times that of the U-0,U-10, U-20, and U-40, respectively. Photoluminescence spectra showed that the photogeneratedelectron-hole recombination rate decreased gradually with the ultrasonic time. Further, the possiblemechanism of photocatalytic process was investigated. This research provides a green, economical andsimple method to modify bismuth oxychloride.
General variational inclusions and General resolvent equations
Zeqing Liu,엄정석,강신민 대한수학회 2004 대한수학회보 Vol.41 No.2
In this paper, we introduce and study a new class ofvariational inclusions, called the general variational inclusion.We prove the equivalence between the general variationalinclusions, the general resolvent equations, and the fixed-pointproblems, using the resolvent operator technique. This equivalenceis used to suggest and analyze a few iterative algorithms forsolving the general variational inclusions and the generalresolvent equations. Under certain conditions, the convergenceanalyses are also studied. The results presentedin this paper generalize, improve and unify anumber of recent results.
Zeqing Liu,김종규,김기홍 대한수학회 2002 대한수학회보 Vol.39 No.3
The purpose of this paper is to introduce the concept ofa class of strictly successively hemicontractive mappingsand construct certain stable and almost stable iterationprocedures for the iterative approximation of fixedpoints for asymptotically nonexpansive and strictlysuccessively hemicontractive mappings in Banach spaces.
COMMON FIXED POINT THEOREMS FOR FOUR MAPPINGS SATISFYING CONTRACTIVE INEQUALITIES OF INTEGRAL TYPE
ZEQING LIU,Miao He,Liangshi Zhao 경남대학교 기초과학연구소 2018 Nonlinear Functional Analysis and Applications Vol.23 No.3
In this paper, three results concerning the existence and uniqueness of common fixed point for four mappings satisfying contractive inequalities of integral type in metric spaces are introduced and proved. And also, we give the three examples.
ZEQING LIU,Lei Meng,Na Liu,CHAHN YONG JUNG 경남대학교 기초과학연구소 2020 Nonlinear Functional Analysis and Applications Vol.25 No.1
Five results involving the existence and uniqueness of common fixed points for mappings satisfying contractive inequalities of integral type in complete metric spaces are proved. And two examples are given. The results presented in this paper generalize or differ from a few results in the literature.
Common fixed points for compatible mappings of type (P) and an application in dynamic programming
Zeqing Liu,Zhenyu Guo,강신민,심수학 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.1
In this paper common fixed point theorems dealing with compatible mappings of type (P) are established. As a application, the existence and uniqueness of common solution for a system of functional equations arising in dynamic programming is given. The results presented in this paper improve, generalize and unify the corresponding results in this field.
COMMON STATIONARY POINTS FOR MULTIVALUED CONTRACTIVE MAPPINGS OF INTEGRAL TYPE WITH δ-DISTANCE
ZEQING LIU,Ying Liu,Shin Min Kang,Lei Meng 경남대학교 기초과학연구소 2018 Nonlinear Functional Analysis and Applications Vol.23 No.3
The existence and uniqueness of stationary points for certain multi-valued con- tractive mappings of integral type with δ-distance in complete metric spaces are established and three illustrative examples are provided. The results presented in this paper extend or differ from several known results in the literature.
Zeqing Liu,Lili Wang,Hyeong Kug Kim,강신민 대한수학회 2008 대한수학회보 Vol.45 No.3
A few sufficient conditions for the existence and uniqueness of fixed point and common fixed point for certain contractive type mappings in complete metric spaces are provided. Several existence and uniqueness results of solution and common solution for some functional equations and system of functional equations in dynamic programming are discussed by using the fixed point and common fixed point theorems presented in this paper. A few sufficient conditions for the existence and uniqueness of fixed point and common fixed point for certain contractive type mappings in complete metric spaces are provided. Several existence and uniqueness results of solution and common solution for some functional equations and system of functional equations in dynamic programming are discussed by using the fixed point and common fixed point theorems presented in this paper.
Generalized Multivalued Quasivariational Inclusions for Fuzzy Mappings
ZEQING LIU,엄정석,강신민 한국수학교육학회 2007 純粹 및 應用數學 Vol.14 No.1
In this paper, we introduce and study a clas of generalized multivaluedquasivariational inclusions for fuzy mapings, and estab lish its equivalence with aclas of uzy xed-point problems by using the resolvent op erator technique. Wesugest a new iterative algorithm for the generalized multivalued quasivariationalinclusions. Further, we stablish a few existence results of solutions for the gen-eralized multivalued quasivariational inclusions involv ing Fr-relaxed Lipschitz andFr-strongly monotone mapings, and iscus the convergence c riteria for the algo-rithm.
ON GENERALIZED NONLINEAR QUASI-VARIATIONAL-LIKE INCLUSIONS DEALING WITH (h, η)-PROXIMAL MAPPING
Zeqing Liu,Zhengsheng Chen,심수학,강신민 대한수학회 2008 대한수학회지 Vol.45 No.5
In this paper, a new class of (h, η)-proximal mappings for proper functionals in Hilbert spaces is introduced. The existence and Lipschitz continuity of the (h, η)-proximal mappings for proper functionals are proved. A class of generalized nonlinear quasi-variational-like inclusions in Hilbert spaces is introduced. A perturbed three-step iterative algorithm with errors for the generalized nonlinear quasi-variational-like inclusion is suggested. The existence and uniqueness theorems of solution for the generalized nonlinear quasi-variational-like inclusion are established. The convergence and stability results of iterative sequence generated by the perturbed three-step iterative algorithm with errors are discussed. In this paper, a new class of (h, η)-proximal mappings for proper functionals in Hilbert spaces is introduced. The existence and Lipschitz continuity of the (h, η)-proximal mappings for proper functionals are proved. A class of generalized nonlinear quasi-variational-like inclusions in Hilbert spaces is introduced. A perturbed three-step iterative algorithm with errors for the generalized nonlinear quasi-variational-like inclusion is suggested. The existence and uniqueness theorems of solution for the generalized nonlinear quasi-variational-like inclusion are established. The convergence and stability results of iterative sequence generated by the perturbed three-step iterative algorithm with errors are discussed.