We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap function...We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap functions under the condition that the involved mapping F is g-strongly monotone with respect to the solution, but not necessarily continuous differentiable, even not locally Lipschitz.展开更多
Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic c...Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic crystals for TE and TM waves are different from the two-dimensional conventional photonic crystals. Some absolute band gaps and semiDirac points are found. When the medium column radius and the function form of the dielectric constant are modulated, the numbers, width, and position of band gaps are changed, and the semi-Dirac point can either occur or disappear. Therefore,the special band gaps structures and semi-Dirac points can be achieved through the modulation on the two-dimensional function photonic crystals. The results will provide a new design method of optical devices based on the two-dimensional function photonic crystals.展开更多
A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable...A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method.展开更多
Starting from presenting and analyzing some information gap activities during the previous teaching experience, this article has inferred the major roles of information gap activities. Some strategies to implement the...Starting from presenting and analyzing some information gap activities during the previous teaching experience, this article has inferred the major roles of information gap activities. Some strategies to implement the information gap activities are also recommended together with the functions of the instructors via these activities. What information gap activities can teach us in TESOL （teaching English for speakers of other languages） is that information gap activities contribute to setting up a climate of a mutual autonomous learning style both for the learners and the instructors, and these activities activate a diversity in the learning atmosphere.展开更多
ZnTi-layered double hydroxides（LDHs） with varying Zn/Ti ratio have been synthesized by coprecipitation of zinc and titanium salts from homogeneous solution.The obtained ZnTi-LDHs possess high crystallinity and hiera...ZnTi-layered double hydroxides（LDHs） with varying Zn/Ti ratio have been synthesized by coprecipitation of zinc and titanium salts from homogeneous solution.The obtained ZnTi-LDHs possess high crystallinity and hierarchical structure with improved UV-absorbance property.The UV-vis spectra show that the UV absorbing properties of ZnTi-LDHs is stronger and broader than both MgAl-LDH and ZnAl-LDH due to the existence of Ti.Moreover,the UV absorption property increased with the content of Ti,which can be ascribed to the decrease in the band gap energy,as clearly confirmed by density functional theory calculations.When irradiated by UV rays,the property of the samples with generated free radicals（OH^·and O2^·） was evaluated by means of electron spin resonance（EPR）.ZnTi-LDHs generated a relatively lower active radicals in contrast with TiO2 and ZnO,which implied an increased safety used as sunscreens.Therefore,this work provides a detailed understanding of UV shielding properties of ZnTiLDHs which was unrevealed previously,and demonstrates the expansive application prospects of ZnTiLDHs in the field of sunscreens.展开更多
By applying the auxiliary variational principle technique, the existence of solutions for a new class of generalized mixed implicit quasi-variational-like inequalities and the convergence criteria of a new iterative a...By applying the auxiliary variational principle technique, the existence of solutions for a new class of generalized mixed implicit quasi-variational-like inequalities and the convergence criteria of a new iterative algorithm to compute approximate solutions are proved in Hilbert spaces. The obtained result is a improvement over and generalization of the main theorem proposed by Ding.展开更多
The formation, structural and electronic properties of silicene oxides（SOs） that result from the oxidation of silicene on Ag（111） surface have been investigated in the framework of density functional theory（DFT）...The formation, structural and electronic properties of silicene oxides（SOs） that result from the oxidation of silicene on Ag（111） surface have been investigated in the framework of density functional theory（DFT）.It is found that the honeycomb lattice of silicene on the Ag（111） surface changes after the oxidation. SOs are strongly hybridized with the Ag（111） surface so that they possess metallic band structures. Charge accumulation between SOs and the Ag（111） surface indicates strong chemical bonding, which dramatically affects the electronic properties of SOs. When SOs are peeled off the Ag（111） surface, however, they may become semiconductors.展开更多
In this paper,by using scalarization techniques and a minimax strategy,error bound results in terms of gap functions for a generalized mixed vector equilibrium problem are established,where the solutions for vector pr...In this paper,by using scalarization techniques and a minimax strategy,error bound results in terms of gap functions for a generalized mixed vector equilibrium problem are established,where the solutions for vector problems may be general sets under natural assumptions,but are not limited to singletons.The other essentially equivalent approach via a separation principle is analyzed.Special cases to the classical vector equilibrium problem and vector variational inequality are also discussed.展开更多
This paper considers a class of stochastic variational inequality problems. As proposed by Jiang and Xu （2008）, by using the so-called regularized gap function, the authors formulate the problems as constrained opti...This paper considers a class of stochastic variational inequality problems. As proposed by Jiang and Xu （2008）, by using the so-called regularized gap function, the authors formulate the problems as constrained optimization problems and then propose a sample average approximation method for solving the problems. Under some moderate conditions, the authors investigate the limiting behavior of the optimal values and the optimal solutions of the approximation problems. Finally, some numerical results are reported to show efficiency of the proposed method.展开更多
基金supported by the National Natural Science Foundation of China (No. 10671050)the Natural Science Foundation of Heilongjiang Province of China (No. A200607)
文摘We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap functions under the condition that the involved mapping F is g-strongly monotone with respect to the solution, but not necessarily continuous differentiable, even not locally Lipschitz.
基金Project supported by the National Natural Science Foundations of China(Grant No.61275047)the Research Project of Chinese Ministry of Education(Grant No.213009A)the Scientific and Technological Development Foundation of Jilin Province,China(Grant No.20130101031JC)
文摘Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic crystals for TE and TM waves are different from the two-dimensional conventional photonic crystals. Some absolute band gaps and semiDirac points are found. When the medium column radius and the function form of the dielectric constant are modulated, the numbers, width, and position of band gaps are changed, and the semi-Dirac point can either occur or disappear. Therefore,the special band gaps structures and semi-Dirac points can be achieved through the modulation on the two-dimensional function photonic crystals. The results will provide a new design method of optical devices based on the two-dimensional function photonic crystals.
基金Project supported by the National Natural Science Foundation of China(Nos.10902077,11172209, and 10572031)
文摘A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method.
文摘Starting from presenting and analyzing some information gap activities during the previous teaching experience, this article has inferred the major roles of information gap activities. Some strategies to implement the information gap activities are also recommended together with the functions of the instructors via these activities. What information gap activities can teach us in TESOL （teaching English for speakers of other languages） is that information gap activities contribute to setting up a climate of a mutual autonomous learning style both for the learners and the instructors, and these activities activate a diversity in the learning atmosphere.
基金supported by the National Natural Science Foundation of China (No. 21301012)the Development of High-Caliber Talents Project of Beijing Municipal Institutions (No. CIT & TCD 201504009)+1 种基金China Cosmetic Collaborative Innovation Center, BTBUthe Open Research Fund Program of Beijing Key Lab of Plant Resource Research and Development, BTBU
文摘ZnTi-layered double hydroxides（LDHs） with varying Zn/Ti ratio have been synthesized by coprecipitation of zinc and titanium salts from homogeneous solution.The obtained ZnTi-LDHs possess high crystallinity and hierarchical structure with improved UV-absorbance property.The UV-vis spectra show that the UV absorbing properties of ZnTi-LDHs is stronger and broader than both MgAl-LDH and ZnAl-LDH due to the existence of Ti.Moreover,the UV absorption property increased with the content of Ti,which can be ascribed to the decrease in the band gap energy,as clearly confirmed by density functional theory calculations.When irradiated by UV rays,the property of the samples with generated free radicals（OH^·and O2^·） was evaluated by means of electron spin resonance（EPR）.ZnTi-LDHs generated a relatively lower active radicals in contrast with TiO2 and ZnO,which implied an increased safety used as sunscreens.Therefore,this work provides a detailed understanding of UV shielding properties of ZnTiLDHs which was unrevealed previously,and demonstrates the expansive application prospects of ZnTiLDHs in the field of sunscreens.
文摘By applying the auxiliary variational principle technique, the existence of solutions for a new class of generalized mixed implicit quasi-variational-like inequalities and the convergence criteria of a new iterative algorithm to compute approximate solutions are proved in Hilbert spaces. The obtained result is a improvement over and generalization of the main theorem proposed by Ding.
基金supported by the National Basic Research Program of China (Grant No. 2013CB632101)the National Natural Science Foundation of China (Grant Nos. 61222404 and 61474097)the Program of the Ministry of Education of China for Innovative Research Teams in Universities (Grant No. IRT13R54)
文摘The formation, structural and electronic properties of silicene oxides（SOs） that result from the oxidation of silicene on Ag（111） surface have been investigated in the framework of density functional theory（DFT）.It is found that the honeycomb lattice of silicene on the Ag（111） surface changes after the oxidation. SOs are strongly hybridized with the Ag（111） surface so that they possess metallic band structures. Charge accumulation between SOs and the Ag（111） surface indicates strong chemical bonding, which dramatically affects the electronic properties of SOs. When SOs are peeled off the Ag（111） surface, however, they may become semiconductors.
基金This research was supported by the National Natural Science Foundation of China(Nos.11301567 and 11571055)the Fundamental Research Funds for the Central Universities(No.106112015CDJXY100002).
文摘In this paper,by using scalarization techniques and a minimax strategy,error bound results in terms of gap functions for a generalized mixed vector equilibrium problem are established,where the solutions for vector problems may be general sets under natural assumptions,but are not limited to singletons.The other essentially equivalent approach via a separation principle is analyzed.Special cases to the classical vector equilibrium problem and vector variational inequality are also discussed.
基金This research is partly supported by the National Natural Science Foundation of China under Grant Nos. 71171027 and 11071028, the Fundamental Research Funds for the Central Universities under Grant No. DUT11SX11, and the Key Project of the National Natural Science Foundation of China under Grant No. 71031002.
文摘This paper considers a class of stochastic variational inequality problems. As proposed by Jiang and Xu （2008）, by using the so-called regularized gap function, the authors formulate the problems as constrained optimization problems and then propose a sample average approximation method for solving the problems. Under some moderate conditions, the authors investigate the limiting behavior of the optimal values and the optimal solutions of the approximation problems. Finally, some numerical results are reported to show efficiency of the proposed method.
