Four phenoxysilicon networks for nonlinear optical (NLO) applications were designed and prepared by an extended sol-gel process without additional H2O and catalyst. All poled polymer network films possess high second-...Four phenoxysilicon networks for nonlinear optical (NLO) applications were designed and prepared by an extended sol-gel process without additional H2O and catalyst. All poled polymer network films possess high second-order nonlinear optical coefficients (d(33)) Of 10(-7)similar to 10(-8) esu. The investigation of NLO temporal stability at room temperature and elevated temperature (120 degreesC) indicated that these films exhibit high d(33) stability because the orientation of the chromophores are locked in the phenoxysilicon organic/inorganic networks.展开更多
In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower soluti...In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower solutions. Our results improve someknown works.展开更多
On the basis of ZINDO method and according to the sum over states(SOS) expression, the program is devised for the calculation of nonlinear second order optical susceptibilites β ijk and studying how ...On the basis of ZINDO method and according to the sum over states(SOS) expression, the program is devised for the calculation of nonlinear second order optical susceptibilites β ijk and studying how different substituents on the phenyl ring attached to the atom silicon influence on the nonlinear second order optical properties of substituted silane series of molecules. The properties of (CH 3) 3Si? ?has been studied particularly. The effect of the length of silica chains on the calculated values has been studied too. The regularity summarized from the calculated results has been explained micromechanically.展开更多
In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some e...In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.展开更多
By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed....By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.展开更多
In this paper, based on a new more general ansitz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution eq...In this paper, based on a new more general ansitz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution equations with nonlinear terms of any order. Compared with most existing tanh methods for finding travelling wave solutions, the proposed method not only recovers the results by most known algebraic methods, but also provides new and more general solutions. We choose the generalized Burgers-Fisher equation with nonlinear terms of any order to illustrate our method. As a result, we obtain several new kinds of exact solutions for the equation. This approach can also be applied to other nonlinear evolution equations with nonlinear terms of any order.展开更多
This paper investigates equation (1) in twocases:(i)P=0, (ii)P satisfies|P (i,x,y,z,w)<(A+|y|+|z|+|w|)q(t).whereq(t) is a nonnegative function of t. For case (i) the asymptotic stability in the large of the trivial...This paper investigates equation (1) in twocases:(i)P=0, (ii)P satisfies|P (i,x,y,z,w)<(A+|y|+|z|+|w|)q(t).whereq(t) is a nonnegative function of t. For case (i) the asymptotic stability in the large of the trivial solution x=0 is investigated and for case (ii) the boundedness result is obtained for solutions of equation (1). These results improve and include several well-known results.展开更多
In this paper, we first present constructing a Lyapunov function for (1. 1) and then we show the asymptotic stability in the large of the trivial solution x=0 for case p≡ 0,and the boundedness result of the sol...In this paper, we first present constructing a Lyapunov function for (1. 1) and then we show the asymptotic stability in the large of the trivial solution x=0 for case p≡ 0,and the boundedness result of the solutions of (1 .1 ) for case p≠0. These results improve sveral well-known results.展开更多
This paper presents a nonlinear profile order scheme for three-dimensional（3D） hybrid radial acquisition applied to self-gated, free-breathing cardiac cine magnetic resonance imaging（MRI）. In self-gated, free-brea...This paper presents a nonlinear profile order scheme for three-dimensional（3D） hybrid radial acquisition applied to self-gated, free-breathing cardiac cine magnetic resonance imaging（MRI）. In self-gated, free-breathing cardiac cine MRI,respiratory and cardiac motions are unpredictable during acquisition, especially for retrospective reconstruction. Therefore,the non-uniformity of the k-space distribution is an issue of great concern during retrospective self-gated reconstruction. A nonlinear profile order with varying azimuthal increments was provided and compared with the existing golden ratio-based profile order. Optimal parameter values for the nonlinear formula were chosen based on simulations. The two profile orders were compared in terms of the k-space distribution and phantom and human image results. An approximately uniform distribution was obtained based on the nonlinear profile order for persons with various heart rates and breathing patterns.The nonlinear profile order provides more stable profile distributions and fewer streaking artifacts in phantom images. In a comparison of human cardiac cine images, the nonlinear profile order provided results comparable to those provided by the golden ratio-based profile order, and the images were suitable for diagnosis. In conclusion, the nonlinear profile order scheme was demonstrated to be insensitive to various motion patterns and more useful for retrospective reconstruction.展开更多
Films were prepared from mixtures of copolymers of 4-nitro-4'-[N-methylacryloyloxyethyl, N'-ethyl] amino azobenzene with glycidyl methacrylate (chromophore content: 6 mol%) and copolymers containing anhydride ...Films were prepared from mixtures of copolymers of 4-nitro-4'-[N-methylacryloyloxyethyl, N'-ethyl] amino azobenzene with glycidyl methacrylate (chromophore content: 6 mol%) and copolymers containing anhydride units, which was obtained by the reaction of 4-nitro-4'-[N-hydroxyethyl, N'-ethyl] amino azobenzene with polymethacryloyl chloride (chromophore content: 25 mol %). During thermal poling process the anhydride reacts with the epoxy group and the resulting crosslinked network structure will stabilize the second harmonic generation in the poled film. The second harmonic generation of the poled film shows a maximum with the variation of composition this is presumed to be due to the effects of the increasing of concentration, orientation order as well as orientation stability of chromophore groups during crosslinking.展开更多
Second order nonlinear optical active 2,3-dichloro-5,6-dicyanopyrazine (DCDCP) and its monoamine-substituted derivatives had been synthesized. Their facile synthesis, high melt point, high incidence af substantial SHG...Second order nonlinear optical active 2,3-dichloro-5,6-dicyanopyrazine (DCDCP) and its monoamine-substituted derivatives had been synthesized. Their facile synthesis, high melt point, high incidence af substantial SHG activity and increased transparency inthe blue and near infrared make this class compounds appealling for further investigation.展开更多
The syntheses and characterization of novel biferrocene trinuclear complexes of Schiff base ligand, S methyl N (ferrocenyl 1 methyl methylidene)dithiocarbazate [hereafter abbreviated as HL (1)], are described. The X r...The syntheses and characterization of novel biferrocene trinuclear complexes of Schiff base ligand, S methyl N (ferrocenyl 1 methyl methylidene)dithiocarbazate [hereafter abbreviated as HL (1)], are described. The X ray diffraction studies have established the structures of PdL 2 (3) and CuL 2 (4). The geometry of Pd(Ⅱ) in (3) is close to a square plane and in the novel cis configuration the two ferrocene moieties are in cis configuration, while that of Cu(Ⅱ) in (4) is close to a tetrahedral configuration. The electrochemical measurements suggested that the square planar configuration of Ni(Ⅱ) and Pd(Ⅱ) moieties can effectively transmit the redox effects of the ferrocene moieties, while the tetrahedral configuration of the Cu(Ⅱ) complex can not transmit the redox effects. The degenerate four wave mixing (DFWM) measurements showed that the complexes exhibit obviously nonlinear optical (NLO) response. The magnitude of their third order NLO susceptibility can be explained by their structure and electrochemical properties.展开更多
Is this Paper, the global existence of smooth solutions to the Antial value problem for the fourth order nonlinear Schrodinger equation in the Lax hierarchy of the nonlinear fSchrodinger equation(NLS equation) is esta...Is this Paper, the global existence of smooth solutions to the Antial value problem for the fourth order nonlinear Schrodinger equation in the Lax hierarchy of the nonlinear fSchrodinger equation(NLS equation) is established by using the so-called continuation method and delicate a priori estimate. In addition, the asylnptotic properties of the solutions as|×|+∞ are discussed.展开更多
Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' +p(t)(y'(t))σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and ...Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' +p(t)(y'(t))σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and q(t) are allowed to change sign on [t0, ∞), and f∈C1 (R, R) such that xf(x) > 0 for x ≠0. Our results improve and extend some known oscillation criteria. Examples are inserted to illustrate our results.展开更多
To deal with stabilizing of nonlinear affine fractional order systems subject to time varying delays,two methods for finding an appropriate pseudo state feedback controller are discussed.In the first method,using the ...To deal with stabilizing of nonlinear affine fractional order systems subject to time varying delays,two methods for finding an appropriate pseudo state feedback controller are discussed.In the first method,using the Mittag-Lefler function,Laplace transform and Gronwall inequality,a linear stabilizing controller is derived,which uses the fractional order of the delayed system and the upper bound of system nonlinear functions.In the second method,at first a sufficient stability condition for the delayed system is given in the form of a simple linear matrix inequality(LMI)which can easily be solved.Then,on the basis of this result,a stabilizing pseudo-state feedback controller is designed in which the controller gain matrix is easily computed by solving an LMI in terms of delay bounds.Simulation results show the effectiveness of the proposed methods.展开更多
Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p（t） and q（t） are allowed to change sign on [t0,∞).
This paper concerns the calculation of the wave trough exceedance probabilities in a nonlinear sea. The calculations have been carried out by incorporating a second order nonlinear wave model into an asymptotic method...This paper concerns the calculation of the wave trough exceedance probabilities in a nonlinear sea. The calculations have been carried out by incorporating a second order nonlinear wave model into an asymptotic method. This is a new approach for the calculation of the wave trough exceedance probabilities, and, as all of the calculations are performed in the probability domain, avoids the need for long time-domain simulations. The proposed asymptotic method has been applied to calculate the wave trough depth exceedance probabilities of a sea state with the surface elevation data measured at the coast of Yura in the Japan Sea. It is demonstrated that the proposed new method can offer better predictions than the theoretical Rayleigh wave trough depth distribution model. The calculated results by using the proposed new method have been further compared with those obtained by using the Arhan and Plaisted nonlinear distribution model and the Toffoli et al.’s wave trough depth distribution model, and its accuracy has been once again substantiated. The research findings obtained from this study demonstrate that the proposed asymptotic method can be readily utilized in the process of designing various kinds of ocean engineering structures.展开更多
P91 steel is an important bearing material used in nuclear power plants. The study of its mechanical degradation behavior is important for ensuring safe operation. The relationship between the dislocation density of P...P91 steel is an important bearing material used in nuclear power plants. The study of its mechanical degradation behavior is important for ensuring safe operation. The relationship between the dislocation density of P91 steel under different strains and the corresponding nonlinear ultrasonic parameter β was studied. The dislocation density of strained samples was estimated by X-ray diffraction. Nonlinear ultrasonic testing was conducted to evaluate β, showing that this value increased with increasing dislocation density induced by different tensile elongations. It was shown that the ultrasonic secondharmonic generation technique can effectively evaluate the degradation behavior of metallic materials, and the prediction of the residual life of bearing parts in service can be made based on β and the dislocation density.展开更多
The title compound of isonicotinato lead（Ⅱ） [Pb（C5H4NCOO）2] has been optimized at B3LYP/LANL2DZ level of theory and calculated results show that the lead（Ⅱ） ion adopts 4-coordinate geometry. Atomic charge dist...The title compound of isonicotinato lead（Ⅱ） [Pb（C5H4NCOO）2] has been optimized at B3LYP/LANL2DZ level of theory and calculated results show that the lead（Ⅱ） ion adopts 4-coordinate geometry. Atomic charge distributions indicate that during forming the title compound, each isonicotinic acid ion transfers -0.452 e to lead（Ⅱ） ion. The electronic spectra calculations show that there exist two absorption bands and the electronic transitions are mainly derived from the contribution of intraligand π→π^＊ transition and ligand-to-metal charge transfer （LMCT） transition. The thermodynamic properties of the title compound at different temperatures have been calculated and corresponding relations between property and temperature have also been obtained. The calculation of the second order optical nonlinearity was carried out, and the molecular hyperpolarizability was 3.62365^＊10^-30 esu.展开更多
文摘Four phenoxysilicon networks for nonlinear optical (NLO) applications were designed and prepared by an extended sol-gel process without additional H2O and catalyst. All poled polymer network films possess high second-order nonlinear optical coefficients (d(33)) Of 10(-7)similar to 10(-8) esu. The investigation of NLO temporal stability at room temperature and elevated temperature (120 degreesC) indicated that these films exhibit high d(33) stability because the orientation of the chromophores are locked in the phenoxysilicon organic/inorganic networks.
文摘In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower solutions. Our results improve someknown works.
文摘On the basis of ZINDO method and according to the sum over states(SOS) expression, the program is devised for the calculation of nonlinear second order optical susceptibilites β ijk and studying how different substituents on the phenyl ring attached to the atom silicon influence on the nonlinear second order optical properties of substituted silane series of molecules. The properties of (CH 3) 3Si? ?has been studied particularly. The effect of the length of silica chains on the calculated values has been studied too. The regularity summarized from the calculated results has been explained micromechanically.
基金supported by the Research Foundation of Education Bureau of Hubei Province,China (Grant No Z200612001)the Natural Science Foundation of Yangtze University (Grant No 20061222)
文摘In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.
文摘By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.
基金The project partially supported by the State Key Basic Research Program of China under Grant No. 2004CB318000
文摘In this paper, based on a new more general ansitz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution equations with nonlinear terms of any order. Compared with most existing tanh methods for finding travelling wave solutions, the proposed method not only recovers the results by most known algebraic methods, but also provides new and more general solutions. We choose the generalized Burgers-Fisher equation with nonlinear terms of any order to illustrate our method. As a result, we obtain several new kinds of exact solutions for the equation. This approach can also be applied to other nonlinear evolution equations with nonlinear terms of any order.
文摘This paper investigates equation (1) in twocases:(i)P=0, (ii)P satisfies|P (i,x,y,z,w)<(A+|y|+|z|+|w|)q(t).whereq(t) is a nonnegative function of t. For case (i) the asymptotic stability in the large of the trivial solution x=0 is investigated and for case (ii) the boundedness result is obtained for solutions of equation (1). These results improve and include several well-known results.
文摘In this paper, we first present constructing a Lyapunov function for (1. 1) and then we show the asymptotic stability in the large of the trivial solution x=0 for case p≡ 0,and the boundedness result of the solutions of (1 .1 ) for case p≠0. These results improve sveral well-known results.
基金supported by the National Natural Science Foundation of China(Grant Nos.81501463,61671026,81571669,and 81671853)the Natural Science Foundation of Guangdong Province,China(Grant No.2014A030310360)+3 种基金Guangdong Innovative Research Team Program of China(Grant No.2011S013)the Basic Research Project of Shenzhen City,China(Grant Nos.JCYJ20140417113430639 and JCYJ20160429172357751)the High-level Oversea Talent Program of Shenzhen City,China(Grant No.KQJSCX20160301144248)Beijing Center for Mathematics and Information Interdisciplinary Sciences of China
文摘This paper presents a nonlinear profile order scheme for three-dimensional（3D） hybrid radial acquisition applied to self-gated, free-breathing cardiac cine magnetic resonance imaging（MRI）. In self-gated, free-breathing cardiac cine MRI,respiratory and cardiac motions are unpredictable during acquisition, especially for retrospective reconstruction. Therefore,the non-uniformity of the k-space distribution is an issue of great concern during retrospective self-gated reconstruction. A nonlinear profile order with varying azimuthal increments was provided and compared with the existing golden ratio-based profile order. Optimal parameter values for the nonlinear formula were chosen based on simulations. The two profile orders were compared in terms of the k-space distribution and phantom and human image results. An approximately uniform distribution was obtained based on the nonlinear profile order for persons with various heart rates and breathing patterns.The nonlinear profile order provides more stable profile distributions and fewer streaking artifacts in phantom images. In a comparison of human cardiac cine images, the nonlinear profile order provided results comparable to those provided by the golden ratio-based profile order, and the images were suitable for diagnosis. In conclusion, the nonlinear profile order scheme was demonstrated to be insensitive to various motion patterns and more useful for retrospective reconstruction.
文摘Films were prepared from mixtures of copolymers of 4-nitro-4'-[N-methylacryloyloxyethyl, N'-ethyl] amino azobenzene with glycidyl methacrylate (chromophore content: 6 mol%) and copolymers containing anhydride units, which was obtained by the reaction of 4-nitro-4'-[N-hydroxyethyl, N'-ethyl] amino azobenzene with polymethacryloyl chloride (chromophore content: 25 mol %). During thermal poling process the anhydride reacts with the epoxy group and the resulting crosslinked network structure will stabilize the second harmonic generation in the poled film. The second harmonic generation of the poled film shows a maximum with the variation of composition this is presumed to be due to the effects of the increasing of concentration, orientation order as well as orientation stability of chromophore groups during crosslinking.
文摘Second order nonlinear optical active 2,3-dichloro-5,6-dicyanopyrazine (DCDCP) and its monoamine-substituted derivatives had been synthesized. Their facile synthesis, high melt point, high incidence af substantial SHG activity and increased transparency inthe blue and near infrared make this class compounds appealling for further investigation.
文摘The syntheses and characterization of novel biferrocene trinuclear complexes of Schiff base ligand, S methyl N (ferrocenyl 1 methyl methylidene)dithiocarbazate [hereafter abbreviated as HL (1)], are described. The X ray diffraction studies have established the structures of PdL 2 (3) and CuL 2 (4). The geometry of Pd(Ⅱ) in (3) is close to a square plane and in the novel cis configuration the two ferrocene moieties are in cis configuration, while that of Cu(Ⅱ) in (4) is close to a tetrahedral configuration. The electrochemical measurements suggested that the square planar configuration of Ni(Ⅱ) and Pd(Ⅱ) moieties can effectively transmit the redox effects of the ferrocene moieties, while the tetrahedral configuration of the Cu(Ⅱ) complex can not transmit the redox effects. The degenerate four wave mixing (DFWM) measurements showed that the complexes exhibit obviously nonlinear optical (NLO) response. The magnitude of their third order NLO susceptibility can be explained by their structure and electrochemical properties.
文摘Is this Paper, the global existence of smooth solutions to the Antial value problem for the fourth order nonlinear Schrodinger equation in the Lax hierarchy of the nonlinear fSchrodinger equation(NLS equation) is established by using the so-called continuation method and delicate a priori estimate. In addition, the asylnptotic properties of the solutions as|×|+∞ are discussed.
文摘Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' +p(t)(y'(t))σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and q(t) are allowed to change sign on [t0, ∞), and f∈C1 (R, R) such that xf(x) > 0 for x ≠0. Our results improve and extend some known oscillation criteria. Examples are inserted to illustrate our results.
文摘To deal with stabilizing of nonlinear affine fractional order systems subject to time varying delays,two methods for finding an appropriate pseudo state feedback controller are discussed.In the first method,using the Mittag-Lefler function,Laplace transform and Gronwall inequality,a linear stabilizing controller is derived,which uses the fractional order of the delayed system and the upper bound of system nonlinear functions.In the second method,at first a sufficient stability condition for the delayed system is given in the form of a simple linear matrix inequality(LMI)which can easily be solved.Then,on the basis of this result,a stabilizing pseudo-state feedback controller is designed in which the controller gain matrix is easily computed by solving an LMI in terms of delay bounds.Simulation results show the effectiveness of the proposed methods.
文摘Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p（t） and q（t） are allowed to change sign on [t0,∞).
文摘?-(2-methylthio -4 -methyl -5 -pyrimidinyl)-2. 4 - pentadiyn- 1 -ol- (4- N. N-dimethylamino-azobenzene -4' -sulfonate) (PDABS - 1 ). ②5 -(2 -methylthio -4 -methyl -5-pyrimidinyl)- 2.4 -pentadiyn- 1 -ol - (azobenzene - 4 -sulfonate) (PDABS -2 ). ③2. 4 -hexadiyn - 1 -ol-6- (4 - N, N-dimethylamino-azobenzene-4'-sulfonate) (HDABS - 1 ), ④2. 4 -hexadiyn - 1-ol -6 - (azobenzene4-sulfonate) (HDABS-2), the four new compounds are synthesize. The structures of the new compounds have been demonstrdted by elemental analysis. IR(KBr). 1H-NMR (CD3CO/TMS),MS. Their X(3), d33. βμ and the fabrication of their polarization orientated thin film also have ben reported in this paper.
基金financially supported by the funding of an independent research project from the Chinese State Key Laboratory of Ocean Engineering(Grant No.GKZD010038)
文摘This paper concerns the calculation of the wave trough exceedance probabilities in a nonlinear sea. The calculations have been carried out by incorporating a second order nonlinear wave model into an asymptotic method. This is a new approach for the calculation of the wave trough exceedance probabilities, and, as all of the calculations are performed in the probability domain, avoids the need for long time-domain simulations. The proposed asymptotic method has been applied to calculate the wave trough depth exceedance probabilities of a sea state with the surface elevation data measured at the coast of Yura in the Japan Sea. It is demonstrated that the proposed new method can offer better predictions than the theoretical Rayleigh wave trough depth distribution model. The calculated results by using the proposed new method have been further compared with those obtained by using the Arhan and Plaisted nonlinear distribution model and the Toffoli et al.’s wave trough depth distribution model, and its accuracy has been once again substantiated. The research findings obtained from this study demonstrate that the proposed asymptotic method can be readily utilized in the process of designing various kinds of ocean engineering structures.
基金Item Sponsored by National Natural Science Foundation of China(61171145,11274226)
文摘P91 steel is an important bearing material used in nuclear power plants. The study of its mechanical degradation behavior is important for ensuring safe operation. The relationship between the dislocation density of P91 steel under different strains and the corresponding nonlinear ultrasonic parameter β was studied. The dislocation density of strained samples was estimated by X-ray diffraction. Nonlinear ultrasonic testing was conducted to evaluate β, showing that this value increased with increasing dislocation density induced by different tensile elongations. It was shown that the ultrasonic secondharmonic generation technique can effectively evaluate the degradation behavior of metallic materials, and the prediction of the residual life of bearing parts in service can be made based on β and the dislocation density.
基金This work was supported by the Natural Science Foundation of Shandong Province (No. Y2002B06)
文摘The title compound of isonicotinato lead（Ⅱ） [Pb（C5H4NCOO）2] has been optimized at B3LYP/LANL2DZ level of theory and calculated results show that the lead（Ⅱ） ion adopts 4-coordinate geometry. Atomic charge distributions indicate that during forming the title compound, each isonicotinic acid ion transfers -0.452 e to lead（Ⅱ） ion. The electronic spectra calculations show that there exist two absorption bands and the electronic transitions are mainly derived from the contribution of intraligand π→π^＊ transition and ligand-to-metal charge transfer （LMCT） transition. The thermodynamic properties of the title compound at different temperatures have been calculated and corresponding relations between property and temperature have also been obtained. The calculation of the second order optical nonlinearity was carried out, and the molecular hyperpolarizability was 3.62365^＊10^-30 esu.
