By using cone-directed contingent derivatives, the unified necessary and sufficient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set-valued optimization.
In this paper, the extremum of second-order directional derivatives, i.e. the gradient of first-order derivatives is discussed. Given second-order directional derivatives in three nonparallel directions, or given seco...In this paper, the extremum of second-order directional derivatives, i.e. the gradient of first-order derivatives is discussed. Given second-order directional derivatives in three nonparallel directions, or given second-order directional derivatives and mixed directional derivatives in two nonparallel directions, the formulae for the extremum of second-order directional derivatives are derived, and the directions corresponding to maximum and minimum are perpendicular to each other.展开更多
The design and the synthesis of two conjugated donor acceptor imidazole derivatives(1, 2) were carried out for second order nonlinear optics. The thermal properties, the transparency and second order nonlinear opti...The design and the synthesis of two conjugated donor acceptor imidazole derivatives(1, 2) were carried out for second order nonlinear optics. The thermal properties, the transparency and second order nonlinear optical properties of the molecules were investigated. The experimental results indicate that a good nonlinearity transparency thermal stability trade off is achieved for them.展开更多
This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related to a type of so-called second-order Sylvester ma...This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related to a type of so-called second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effectiveness of the proposed approaches. Keywords Second-order linear systems - Eigenstructure assignment - Proportional plus derivative feedback - Parametric solution - Singular value decompoition - Right factorization This work was supported in part by the Chinese Outstanding Youth Foundation (No.69504002).展开更多
In this paper, we introduce the concept of second-order compound contingent epiderivative for set-valued maps and discuss its relationship to the second-order contingent epiderivative. Simultaneously, we also investig...In this paper, we introduce the concept of second-order compound contingent epiderivative for set-valued maps and discuss its relationship to the second-order contingent epiderivative. Simultaneously, we also investigate some special properties of the second-order compound contingent epiderivative. By virtue of the second-order compound contingent epiderivative, we establish some unified second-order sufficient and necessary optimality conditions for set-valued optimization problems. All results in this paper generalize the corresponding results in the literature.展开更多
The second-order nonlinear optical properties of thiophene S,S -dioxides derivatives were studied by using the ZINDO-SOS method. The computed results show that the thiophene S,S -dioxide derivatives exhibit larger sec...The second-order nonlinear optical properties of thiophene S,S -dioxides derivatives were studied by using the ZINDO-SOS method. The computed results show that the thiophene S,S -dioxide derivatives exhibit larger second-order polarizabilities than their thiophene precursors. In order to clarify the origin of the different NLO responses among these chromophores, their electron properties and frontier orbital properties were investigated as well. These thiophene S,S -dioxides derivatives are good candidates for their application in electro-optical device due to their high nonlinearities, good thermal and photo stabilities.展开更多
In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional d...In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional derivatives. The result extends the corresponding result of [D. Bednarik and K. Pastor, Math. Program. Ser. A, 113（2008）, 283-298] to constrained optimization problems.展开更多
alculations of the nonlinear second-order optical susceptlbilities(β_(ijk))for sub- stituted tl1iophene derivative;with quinoidlike conformation are reported.These systetems possess small dipole moment;and large diff...alculations of the nonlinear second-order optical susceptlbilities(β_(ijk))for sub- stituted tl1iophene derivative;with quinoidlike conformation are reported.These systetems possess small dipole moment;and large differences between dipole mo- ments of ground and first-excited states.Geometry optimizations of the molecules investigated were carried out using AM 1 method.The calculations were performed using INDO/CI method comboned with a sum-over-states expression for β_(jik). The calculated results sbw that the second-order susceptibility is a function of the na- ture and location of substituents and is larger for disubstituted molecules than monosubstituted molecules. Bipolymeric thiophenemetmne with NH_2/NO_2 groups was calctilated to have a β_μof 79. 920 × 10￣(-30) esu. It was found that the NH_2 and NO_2 groups in above disubstituted molecules are pull-pull groups in ground states,but are usual push-pull groups in the first excited states.展开更多
The second-order nonlinear optical (NLO) properties of a series of benzothiazole derivatives were studied by use of the ZINDO-SOS method. These chromophores are formed by a donor-π-bridge-acceptor system, based on a ...The second-order nonlinear optical (NLO) properties of a series of benzothiazole derivatives were studied by use of the ZINDO-SOS method. These chromophores are formed by a donor-π-bridge-acceptor system, based on a nitro group connected with benzothiazole as the acceptor and a hydroxyl-functional amino group as the donor. For the purpose of comparison, we also designed molecules in which nitrobenzene is an acceptor. The calculation results indicate that benzothiazole derivatives exhibit larger second-order polarizabilities than nitrobenzene derivatives. In order to clarify the origin of the NLO response of these chromophores, their electron properties were investigated as well. The benzothiazole derivatives are good candidates for application in electro-optical device due to their high optical nonlinearities, good thermal and photonic stability.展开更多
On the basis of ZINDO methods, according to the sum-overstates (SOS) expression, the program for the calculation of the second-order nonlinear optical susceptibilities βijk and βμ of molecules was devised, and the ...On the basis of ZINDO methods, according to the sum-overstates (SOS) expression, the program for the calculation of the second-order nonlinear optical susceptibilities βijk and βμ of molecules was devised, and the structures and nonlinear optical properties of unsymmetric bis(phenylethynyl) benzene series derivatives were studied. The influence of the molecular conjugated chain lengths, the donor and the acceptor on βμ was examined.展开更多
基金Supported by the National Natural Science Foundation of China (10571035)
文摘By using cone-directed contingent derivatives, the unified necessary and sufficient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set-valued optimization.
基金Supported by the National Natural Science Foundation of China (10871029,11071025)the Foundation of CAEP (2010A0202010)the Foundation of National Key Laboratory of Science and Technology on Computational Physics
文摘In this paper, the extremum of second-order directional derivatives, i.e. the gradient of first-order derivatives is discussed. Given second-order directional derivatives in three nonparallel directions, or given second-order directional derivatives and mixed directional derivatives in two nonparallel directions, the formulae for the extremum of second-order directional derivatives are derived, and the directions corresponding to maximum and minimum are perpendicular to each other.
基金Supported by the Natural Science Foundation of Hubei ProvinceChina(No.2 0 0 0 J15 6 )
文摘The design and the synthesis of two conjugated donor acceptor imidazole derivatives(1, 2) were carried out for second order nonlinear optics. The thermal properties, the transparency and second order nonlinear optical properties of the molecules were investigated. The experimental results indicate that a good nonlinearity transparency thermal stability trade off is achieved for them.
文摘This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related to a type of so-called second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effectiveness of the proposed approaches. Keywords Second-order linear systems - Eigenstructure assignment - Proportional plus derivative feedback - Parametric solution - Singular value decompoition - Right factorization This work was supported in part by the Chinese Outstanding Youth Foundation (No.69504002).
基金Supported in part by the National Natural Science Foundation of China under Grant No.11601437,11526165and 11571055the Scientific Research Fund of Sichuan Provincial Science and Technology Department under Grant No.2015JY0237the Fundamental Research Funds for the Central Universities under Grant No.JBK160129
文摘In this paper, we introduce the concept of second-order compound contingent epiderivative for set-valued maps and discuss its relationship to the second-order contingent epiderivative. Simultaneously, we also investigate some special properties of the second-order compound contingent epiderivative. By virtue of the second-order compound contingent epiderivative, we establish some unified second-order sufficient and necessary optimality conditions for set-valued optimization problems. All results in this paper generalize the corresponding results in the literature.
基金Supported by the National Natural Science Foundation of China(No. 2 98730 2 5 )
文摘The second-order nonlinear optical properties of thiophene S,S -dioxides derivatives were studied by using the ZINDO-SOS method. The computed results show that the thiophene S,S -dioxide derivatives exhibit larger second-order polarizabilities than their thiophene precursors. In order to clarify the origin of the different NLO responses among these chromophores, their electron properties and frontier orbital properties were investigated as well. These thiophene S,S -dioxides derivatives are good candidates for their application in electro-optical device due to their high nonlinearities, good thermal and photo stabilities.
基金The Graduate Students Innovate Scientific Research Program (YJSCX2008-158HLJ) of Heilongjiang Provincesupported by the Distinguished Young Scholar Foundation (JC200707) of Heilongjiang Province of China
文摘In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional derivatives. The result extends the corresponding result of [D. Bednarik and K. Pastor, Math. Program. Ser. A, 113（2008）, 283-298] to constrained optimization problems.
文摘alculations of the nonlinear second-order optical susceptlbilities(β_(ijk))for sub- stituted tl1iophene derivative;with quinoidlike conformation are reported.These systetems possess small dipole moment;and large differences between dipole mo- ments of ground and first-excited states.Geometry optimizations of the molecules investigated were carried out using AM 1 method.The calculations were performed using INDO/CI method comboned with a sum-over-states expression for β_(jik). The calculated results sbw that the second-order susceptibility is a function of the na- ture and location of substituents and is larger for disubstituted molecules than monosubstituted molecules. Bipolymeric thiophenemetmne with NH_2/NO_2 groups was calctilated to have a β_μof 79. 920 × 10￣(-30) esu. It was found that the NH_2 and NO_2 groups in above disubstituted molecules are pull-pull groups in ground states,but are usual push-pull groups in the first excited states.
基金ProjectsupportedbytheNationalNaturalScienceFoundationofChina (No .2 99730 10 )andtheKeyLabofSupramolecularStructureandMate rialofJilinUniversity .
文摘The second-order nonlinear optical (NLO) properties of a series of benzothiazole derivatives were studied by use of the ZINDO-SOS method. These chromophores are formed by a donor-π-bridge-acceptor system, based on a nitro group connected with benzothiazole as the acceptor and a hydroxyl-functional amino group as the donor. For the purpose of comparison, we also designed molecules in which nitrobenzene is an acceptor. The calculation results indicate that benzothiazole derivatives exhibit larger second-order polarizabilities than nitrobenzene derivatives. In order to clarify the origin of the NLO response of these chromophores, their electron properties were investigated as well. The benzothiazole derivatives are good candidates for application in electro-optical device due to their high optical nonlinearities, good thermal and photonic stability.
基金Project supported by the National Natural Science Foundation of China (Nos. 29890210, 29573104) and the Key Laboratory for Supramolecular Structure and Spectroscopy of Jilin Universtiy.
文摘On the basis of ZINDO methods, according to the sum-overstates (SOS) expression, the program for the calculation of the second-order nonlinear optical susceptibilities βijk and βμ of molecules was devised, and the structures and nonlinear optical properties of unsymmetric bis(phenylethynyl) benzene series derivatives were studied. The influence of the molecular conjugated chain lengths, the donor and the acceptor on βμ was examined.
基金This research was supported by the National Natural Science Foundation of China (10261005)Colleges and Universities' Science and Technology Development Foundation (20040401) of Tianjin
