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
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
A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different ...A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different complex nonsmooth/discontinuous interfaces, we develop an R(x)-orthonormal theory, where R(x) is an integrable flexural rigidity function. The R(x)-orthonormal bases in the linear space of boundary functions are constructed, of which the second-order derivatives of the boundary functions are asked to be orthonormal with respect to the weight function R(x). When the vibration modes of the symmetric composite beam are expressed in terms of the R(x)-orthonormal bases we can derive an eigenvalue problem endowed with a special structure of the coefficient matrix A :=[aij ],aij= 0 if i + j is odd. Based on the special structure we can prove two new theorems, which indicate that the characteristic equation of A can be decomposed into the product of the characteristic equations of two sub-matrices with dimensions half lower. Hence, we can sequentially solve the natural frequencies in closed-form owing to the specialty of A. We use this powerful new theory to analyze the free vibration performance and the vibration modes of symmetric composite beams with three different interfaces.展开更多
In this paper, we present a blind steganalysis based on feature fusion. Features based on Short Time Fourier Transform (STFT), which consists of second-order derivative spectrum features of audio and Mel-frequency cep...In this paper, we present a blind steganalysis based on feature fusion. Features based on Short Time Fourier Transform (STFT), which consists of second-order derivative spectrum features of audio and Mel-frequency cepstrum coefficients, audio quality metrics and features on linear prediction residue are extracted separately. Then feature fusion is conducted. The performance of the proposed steganalysis is evaluated against 4 steganographic schemes: Direct Sequence Spread Spectrum (DSSS), Quantization Index Modulation (QIM), ECHO embedding (ECHO), and Least Significant Bit em-bedding (LSB). Experiment results show that the classifying performance of the proposed detector is much superior to the previous work. Even more exciting is that the proposed methodology could detect the four steganography, with 85%+ classification accuracy achieved in all the detections, which makes the proposed steganalysis methodology capable of being regarded as a blind steganalysis, and especially useful when the steganalyzer are without the knowledge of the steganographic scheme employed in data embedding.展开更多
Twenty 10-hydrocarbylacridones and 2-methylacridone, 1-hydroxyacridone were synthesized from acridone and characterized by mp, IR, UV, 1H NMR and MS. Using Nd:YAG as a laser source, the second-order harmonic generatio...Twenty 10-hydrocarbylacridones and 2-methylacridone, 1-hydroxyacridone were synthesized from acridone and characterized by mp, IR, UV, 1H NMR and MS. Using Nd:YAG as a laser source, the second-order harmonic generation (SHG) values of the acridone derivatives were measured in powder state as compared with urea powder. The results showed that the SHG values of some of 10-hydrocarbylacridones were higher than that of urea, while others were lower. Although the hydrocarbyl substituents (R) attached to nitrogen atom of acridone were different in size and electronegativity, they had a little effect on the SHG values of 10-hydrocarbylacridones. Substituents, such as methyl or hydroxy group connected to the phenyl ring, caused a little effect on the SHG values, too, compared with acrid one. The ability of R to push electron toward the nitrogen atom or to pull electron from the nitrogen atom play an important role on the maximum wavelengths of UV-visible absorption of acridone derivatives.展开更多
In this paper we study optimization problems involving convex nonlinear semidefinite programming(CSDP).Here we convert CSDP into eigenvalue problem by exact penalty function,and apply the U-Lagrangian theory to the fu...In this paper we study optimization problems involving convex nonlinear semidefinite programming(CSDP).Here we convert CSDP into eigenvalue problem by exact penalty function,and apply the U-Lagrangian theory to the function of the largest eigenvalues,with matrix-convex valued mappings.We give the first-and second-order derivatives of U-Lagrangian in the space of decision variables Rm when transversality condition holds.Moreover,an algorithm frame with superlinear convergence is presented.Finally,we give one application:bilinear matrix inequality(BMI)optimization;meanwhile,list their UV decomposition results.展开更多
In this article we prove that some of the sufficient and necessary optimality conditions obtained by Ginchev, Guerraggio, Luc [Appl. Math., 51, 5-36 （2006）] generalize （strictly） those presented by Guerraggio, Luc...In this article we prove that some of the sufficient and necessary optimality conditions obtained by Ginchev, Guerraggio, Luc [Appl. Math., 51, 5-36 （2006）] generalize （strictly） those presented by Guerraggio, Luc [J. Optim. Theory Appl., 109, 615-629 （2001）]. While the former paper shows examples for which the conditions given there are effective but the ones from the latter paper fail, it does not prove that generally the conditions it proposes are stronger. In the present note we complete this comparison with the lacking proof.展开更多
This study is aimed at improving multiple adaptive subtraction.We propose a modified pseudomulti-channel matching method based on the Huber norm,to adjust the matching differences on frequency and phase between the pr...This study is aimed at improving multiple adaptive subtraction.We propose a modified pseudomulti-channel matching method based on the Huber norm,to adjust the matching differences on frequency and phase between the predicted multi-ples and original data.The second-order derivative of the predicted multiples is utilized to replace the derivative of its Hilbert transform.Due to the additional frequency term,this method can enhance the high-frequency component.We introduce 180◦phase rotation of the multiple channels,which can decrease phase differences.The Huber norm interpolates between smooth L2 norm treatment of small residuals and robust L1 norm treatment of large residuals.This method can eliminate the restriction of large value conditions from the L2 norm and weaken the condition of orthogonality from the L1 norm.The applications of the Pluto and Delft models shows that compared with pseudomulti-channel matching filter,the main frequency is increased from 36 Hz to 38 Hz,and the primary reflection wave is more concentrated.The practical application of field data verifies the effectiveness of the proposed method.展开更多
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 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.
文摘A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different complex nonsmooth/discontinuous interfaces, we develop an R(x)-orthonormal theory, where R(x) is an integrable flexural rigidity function. The R(x)-orthonormal bases in the linear space of boundary functions are constructed, of which the second-order derivatives of the boundary functions are asked to be orthonormal with respect to the weight function R(x). When the vibration modes of the symmetric composite beam are expressed in terms of the R(x)-orthonormal bases we can derive an eigenvalue problem endowed with a special structure of the coefficient matrix A :=[aij ],aij= 0 if i + j is odd. Based on the special structure we can prove two new theorems, which indicate that the characteristic equation of A can be decomposed into the product of the characteristic equations of two sub-matrices with dimensions half lower. Hence, we can sequentially solve the natural frequencies in closed-form owing to the specialty of A. We use this powerful new theory to analyze the free vibration performance and the vibration modes of symmetric composite beams with three different interfaces.
基金Supported by the National Natural Science Foundation of China(No.61071173)
文摘In this paper, we present a blind steganalysis based on feature fusion. Features based on Short Time Fourier Transform (STFT), which consists of second-order derivative spectrum features of audio and Mel-frequency cepstrum coefficients, audio quality metrics and features on linear prediction residue are extracted separately. Then feature fusion is conducted. The performance of the proposed steganalysis is evaluated against 4 steganographic schemes: Direct Sequence Spread Spectrum (DSSS), Quantization Index Modulation (QIM), ECHO embedding (ECHO), and Least Significant Bit em-bedding (LSB). Experiment results show that the classifying performance of the proposed detector is much superior to the previous work. Even more exciting is that the proposed methodology could detect the four steganography, with 85%+ classification accuracy achieved in all the detections, which makes the proposed steganalysis methodology capable of being regarded as a blind steganalysis, and especially useful when the steganalyzer are without the knowledge of the steganographic scheme employed in data embedding.
基金Project supported by the SeientificTechnical Commission of Guangzhou (No. 98-J-013-01)the National Natural Science Foundation for Doctors of Guangdong Province.
文摘Twenty 10-hydrocarbylacridones and 2-methylacridone, 1-hydroxyacridone were synthesized from acridone and characterized by mp, IR, UV, 1H NMR and MS. Using Nd:YAG as a laser source, the second-order harmonic generation (SHG) values of the acridone derivatives were measured in powder state as compared with urea powder. The results showed that the SHG values of some of 10-hydrocarbylacridones were higher than that of urea, while others were lower. Although the hydrocarbyl substituents (R) attached to nitrogen atom of acridone were different in size and electronegativity, they had a little effect on the SHG values of 10-hydrocarbylacridones. Substituents, such as methyl or hydroxy group connected to the phenyl ring, caused a little effect on the SHG values, too, compared with acrid one. The ability of R to push electron toward the nitrogen atom or to pull electron from the nitrogen atom play an important role on the maximum wavelengths of UV-visible absorption of acridone derivatives.
基金supported by the National Natural Science Foundation of China(Nos.11701063,11901075)the Project funded by China Postdoctoral Science Foundation(Nos.2019M651091,2019M661073)+5 种基金the Fundamental Research Funds for the Central Universities(Nos.3132021193,3132021199)the Natural Science Foundation of Liaoning Province in China Doctoral Startup Foundation of Liaoning Province in China(Nos.2020-BS-074)Dalian Youth Science and Technology Star(No.2020RQ047)Huzhou Science and Technology Plan(No.2016GY03)Key Research and Development Projects of Shandong Province(No.2019GGX104089)the Natural Science Foundation of Shandong Province(No.ZR2019BA014).
文摘In this paper we study optimization problems involving convex nonlinear semidefinite programming(CSDP).Here we convert CSDP into eigenvalue problem by exact penalty function,and apply the U-Lagrangian theory to the function of the largest eigenvalues,with matrix-convex valued mappings.We give the first-and second-order derivatives of U-Lagrangian in the space of decision variables Rm when transversality condition holds.Moreover,an algorithm frame with superlinear convergence is presented.Finally,we give one application:bilinear matrix inequality(BMI)optimization;meanwhile,list their UV decomposition results.
基金Supported by the Council of Czech Government (MSM 6198959214)
文摘In this article we prove that some of the sufficient and necessary optimality conditions obtained by Ginchev, Guerraggio, Luc [Appl. Math., 51, 5-36 （2006）] generalize （strictly） those presented by Guerraggio, Luc [J. Optim. Theory Appl., 109, 615-629 （2001）]. While the former paper shows examples for which the conditions given there are effective but the ones from the latter paper fail, it does not prove that generally the conditions it proposes are stronger. In the present note we complete this comparison with the lacking proof.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.300102268212)Postdoctoral Science Foundation(2013M540756,2014T70925)and Shaanxi Natural Science Foundation(2014JQ2-4019).
文摘This study is aimed at improving multiple adaptive subtraction.We propose a modified pseudomulti-channel matching method based on the Huber norm,to adjust the matching differences on frequency and phase between the predicted multi-ples and original data.The second-order derivative of the predicted multiples is utilized to replace the derivative of its Hilbert transform.Due to the additional frequency term,this method can enhance the high-frequency component.We introduce 180◦phase rotation of the multiple channels,which can decrease phase differences.The Huber norm interpolates between smooth L2 norm treatment of small residuals and robust L1 norm treatment of large residuals.This method can eliminate the restriction of large value conditions from the L2 norm and weaken the condition of orthogonality from the L1 norm.The applications of the Pluto and Delft models shows that compared with pseudomulti-channel matching filter,the main frequency is increased from 36 Hz to 38 Hz,and the primary reflection wave is more concentrated.The practical application of field data verifies the effectiveness of the proposed method.
