The microstructure evolution and properties of an Al-Zn-Mg-Cu alloy were investigated under different non-linear cooling processes from the solution temperature, combined with in-situ electrical resistivity measuremen...The microstructure evolution and properties of an Al-Zn-Mg-Cu alloy were investigated under different non-linear cooling processes from the solution temperature, combined with in-situ electrical resistivity measurements, selected area diffraction patterns (SADPs), transmission electron microscopy (TEM), and tensile tests. The relative resistivity was calculated to characterize the phase transformation of the experimental alloy during different cooling processes. The results show that at high temperatures, the microstructure evolutions change from the directional diffusion of Zn and Mg atoms to the precipitation of S phase, depending on the cooling rate. At medium temperatures, q phase nucleates on A13Zr dispersoids and grain boundaries under fast cooling conditions, while S phase precipitates under the slow cooling conditions. The strength and ductility of the aged alloy suffer a significant deterioration due to the heterogeneous precipitation in medium temperature range. At low temperatures, homogeneously nucleated GP zone, η′ and η phases precipitate.展开更多
A solid/liquid continuous casting and composite technology was used to produce d8.5 mm brass cladding pure copper stranded wire composite billet and the composite billet was then drawn. The results showed that the com...A solid/liquid continuous casting and composite technology was used to produce d8.5 mm brass cladding pure copper stranded wire composite billet and the composite billet was then drawn. The results showed that the composite billet had good surface quality, metallurgical bonding interface between brass and pure copper as well as elongation of 53.1%. Synergistic deformation degree between pure copper wire and brass cladding layer was high during drawing. With an increase of the total deformation amount, the plastic deformation of the pure copper wire reduced triangular arc gaps between the pure copper wires and the triangular arc gaps were fully filled at 50%. When the total deformation amount was increased to 63%, dislocation cells and microbands successively formed in the pure copper wire. In the brass cladding layer, planar dislocation networks, twins and shear bands formed successively, and the main deformation mechanisms were dislocation sliding, twinning and shear deformation. The tensile strength increased from 240 MPa of the composite billet to 519 MPa of the one with the deformation amount of 63%, but the elongation decreased from 53.1% to 3.2%. A process of solid/liquid continuous casting and composite forming→drawing can work as a new compact method to produce brass cladding pure copper stranded wire composite as railway through grounding wire.展开更多
Using the finite element method and Cole-Cole model for dual-frequency IP method to research numerical simulation, the authors introduced the fundamental principle of the dual-frequency IP method and the boundary valu...Using the finite element method and Cole-Cole model for dual-frequency IP method to research numerical simulation, the authors introduced the fundamental principle of the dual-frequency IP method and the boundary value problem and variational equations, then replaced the complex resistivity of the model with the Cole-Cole model's parameters under ignoring the EM effect. Through solving the last linear equations, electric potentials of all the model's points were obtained. With changing model's parameters, the authors got different curves of the Fs and phases. According to the results of the simulation, the algorithm is proved to be correct and adaptable.展开更多
This paper presented a registration method based on Fourier transform for multi-band images which is involved in translation and small rotation. Although different band images differ a lot in the intensity and feature...This paper presented a registration method based on Fourier transform for multi-band images which is involved in translation and small rotation. Although different band images differ a lot in the intensity and features, they contain certain common information which we can exploit. A model was given that the multi-band images have linear correlations under the least-square sense. It is proved that the coefficients have no effect on the registration progress if two images have linear correlations. Finally, the steps of the registration method were proposed. The experiments show that the model is reasonable and the results are satisfying.展开更多
In this paper, we introduce a new invariant set Eo={u:ux=f'(x)F(u)+ε[g'(x)-f'(x)g(x)]F(u)×exp(-∫^u1/F(z)dz)}where f and g are some smooth functions of x, ε is a constant, and F is a smooth...In this paper, we introduce a new invariant set Eo={u:ux=f'(x)F(u)+ε[g'(x)-f'(x)g(x)]F(u)×exp(-∫^u1/F(z)dz)}where f and g are some smooth functions of x, ε is a constant, and F is a smooth function to be determined. The invariant sets and exact sohltions to nonlinear diffusion equation ut = ( D(u)ux)x + Q(x, u)ux + P(x, u), are discussed. It is shown that there exist several classes of solutions to the equation that belong to the invariant set Eo.展开更多
In this paper, the generator set of R 〈 x1,x2 〉G is obtained in according to the group G = Gl(n,R). The conditions of G = Gl(n, R) -equivalence of a pair of curves are found in terms of G = Gl(n, R)-invariants...In this paper, the generator set of R 〈 x1,x2 〉G is obtained in according to the group G = Gl(n,R). The conditions of G = Gl(n, R) -equivalence of a pair of curves are found in terms of G = Gl(n, R)-invariants. And the independence of GL(n, R) -invariants is shown.展开更多
The actinomycete populations and functions in cadmium (Cd) contaminated soil were investigated by the cultivation- independent molecular methods. The genomic DNA was extracted and purified from soil adulterated with...The actinomycete populations and functions in cadmium (Cd) contaminated soil were investigated by the cultivation- independent molecular methods. The genomic DNA was extracted and purified from soil adulterated with various con- centrations of Cd in the laboratory. The partial 16S rDNA genes were amplified by polymerase chain reaction (PCR) using specific primers bound to evolutionarily conserved regions within these actinomycete genes. The diversity in PCR- amplified products, as measured by denaturing gradient gel electrophoresis (EGGE), was used as a genetic fingerprint of the population. Principle component analysis and Shannon-Weaver diversity index (H) analyses were used to analyze the DGGE results. Results showed that the two principal components accounted for only a low level of the total variance. The value H in contaminated soil was lower than that in the control at later stages of cultivation, whereas at earlier stages it was higher. Among the six sampling time points, the first, fifth and sixth weeks had the highest values of H. Significantly negative correlations between bioavallable Cd concentration and H values existed in the samples from weeks 2 (R = 0.929, P 〈 0.05) and 4 (R = 0.909, P 〈 0.05). These results may shed light on the effect of Cd on the soil environment and the chemical behavior and toxicity of Cd to actinomycetes.展开更多
New classes of exact solutions of the quasi-linear diffusion-reaction equations are obtained by seeking for the high-order conditional Lie-Baeklund symmetries of the considered equations. The method used here extends ...New classes of exact solutions of the quasi-linear diffusion-reaction equations are obtained by seeking for the high-order conditional Lie-Baeklund symmetries of the considered equations. The method used here extends the approaches of derivative-dependent functional separation of variables and the invariant subspace. Behavior to some solutions such as blow-up and quenching is also described.展开更多
In the period 2003-2011, lightning over-voltages accounted for about 47% of the total number of distribution transformer failures observed in the service area ofAES Sul, a power company that operates in the state of R...In the period 2003-2011, lightning over-voltages accounted for about 47% of the total number of distribution transformer failures observed in the service area ofAES Sul, a power company that operates in the state of Rio Grande doSul, in South Brazil. This paper presents the results of an investigation on the influence of the distance between transformer and MV arresters on the surges at the transformer windings caused by direct strikes to the MV network. The analysis, performed through simulations using the Alternative Transients Program, shows that in general higher voltages are produced by subsequent strokes. Although in relation to the primary side the surges transferred to the secondary are much less affected by the distance between transformers and primary arresters, such distance should always be kept as short as possible in order to reduce the probability of occurrence of transformer failures due to over-voltages at the MV bushings.展开更多
A new image encryption approach is proposed.First,a sort transformation based on nonlinear chaoticalgorithm is used to shuffle the positions of image pixels.Then the states of hyper-chaos are used to change the greyva...A new image encryption approach is proposed.First,a sort transformation based on nonlinear chaoticalgorithm is used to shuffle the positions of image pixels.Then the states of hyper-chaos are used to change the greyvalues of the shuffled image according to the changed chaotic values of the same position between the above nonlinearchaotic sequence and the sorted chaotic sequence.The experimental results demonstrate that the image encryptionscheme based on a shuffling map shows advantages of large key space and high-level security.Compared with someencryption algorithms,the suggested encryption scheme is more secure.展开更多
The hot deformation behavior of Ti-6Al-4V (TC4) titanium alloy was investigated in the temperature range from 650℃ to 950℃ with the strain rate ranging from 7.7×10^-4 s^-1 to 7.7×10^-2 s^-1. The hot tens...The hot deformation behavior of Ti-6Al-4V (TC4) titanium alloy was investigated in the temperature range from 650℃ to 950℃ with the strain rate ranging from 7.7×10^-4 s^-1 to 7.7×10^-2 s^-1. The hot tension test results indicate that the flow stress decreases with increasing the deformation temperature and increases with increasing the strain rate. XRD analysis result reveals that only deformation temperature affects the phase constitution. The microstructure evolution under different deformation conditions was characterized by TEM observation. For the deformation of TC4 alloy, the work-hardening is dominant at low temperature, while the dynamic recovery and dynamic re-crystallization assisted softening is dominant at high temperature.展开更多
With the increasingly widespread application of linear algebra theory, and in its opposite direction is not enough emphasis, linear algebra, several important points: matrix, determinant, linear equations, linear tra...With the increasingly widespread application of linear algebra theory, and in its opposite direction is not enough emphasis, linear algebra, several important points: matrix, determinant, linear equations, linear transformations, matrix keratosis and other anti-deepening understanding of the basics and improve the comprehensive ability to solve problems.展开更多
The proof system, based on resolution method, has become quite popular in automatic theorem proving, because this method is simple to implement. At present many kinds of extensions for resolution method are known: Re...The proof system, based on resolution method, has become quite popular in automatic theorem proving, because this method is simple to implement. At present many kinds of extensions for resolution method are known: Resolution with restricted number of variables in disjuncts, resolution over Linear Equations, Cutting planes, etc. For Classical, Intuitionistic and Minimal (Johansson's) propositional logics, the authors introduce the family of resolution systems with full substitution rule (SRC, SRI and SRM) and with e-restricted substitution rule (SeRC, SeRf and SeRM), where the number of substituted formula connectives is bounded by . The authors show that for each of mentioned logic the SR-type system (in tree form) is polynomially equivalent to Frege systems by size, but for every ~' 〉 0, Se+lR-type has exponential speed-up over the SeR-type (in tree form).展开更多
In order to enhance forecasting precision of problems about nonlinear time series in a complex industry system,a new nonlinear fuzzy adaptive variable weight combined forecasting model was established by using concept...In order to enhance forecasting precision of problems about nonlinear time series in a complex industry system,a new nonlinear fuzzy adaptive variable weight combined forecasting model was established by using conceptions of the relative error,the change tendency of the forecasted object,gray basic weight and adaptive control coefficient on the basis of the method of fuzzy variable weight.Based on Visual Basic 6.0 platform,a fuzzy adaptive variable weight combined forecasting and management system was developed.The application results reveal that the forecasting precisions from the new nonlinear combined forecasting model are higher than those of other single combined forecasting models and the combined forecasting and management system is very powerful tool for the required decision in complex industry system.展开更多
The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with "slow" decay initial data. By con...The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with "slow" decay initial data. By constructing an example, first it is illustrated that the classical solution to this kind of Cauchy problem may blow up in a finite time, even if the system is weakly linearly degenerate. Then some lower bounds of the life-span of classical solutions are given in the case that the system is weakly linearly degenerate. These estimates imply that, when the system is weakly linearly degenerate, the classical solution exists almost globally in time. Finally, it is proved that Theorems 1.1-1.3 in [2] are still valid for this kind of initial data.展开更多
Based on the test data of frictional materials and previous research achievements in this field, a generalized non-linear strength theory (GNST) is proposed. It describes non-linear strength properties on the π-plane...Based on the test data of frictional materials and previous research achievements in this field, a generalized non-linear strength theory (GNST) is proposed. It describes non-linear strength properties on the π-plane and the meridian plane using a unified formula, and it includes almost all the present non-linear strength theories, which can be used in just one material. The shape of failure function of the GNST is a smooth curve between the SMP criterion and the Mises criterion on the π-plane, and an exponential curve on the meridian plane. Through the transformed stress space based on the GNST, the combination of the GNST and various constitutive models using p and q as stress parameters can be realized simply and rationally in three-dimensional stress state. Keywords generalized non-linear strength theory (GNST) - transformed stress - constitutive model - application展开更多
We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon- cave regul...We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon- cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of o(√n), where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures.展开更多
The multi-pulse orbits and chaotic dynamics of a simply supported laminated composite piezoelectric rectangular plate under combined parametric excitation and transverse excitation are studied in detail. It is assumed...The multi-pulse orbits and chaotic dynamics of a simply supported laminated composite piezoelectric rectangular plate under combined parametric excitation and transverse excitation are studied in detail. It is assumed that different layers are perfectly bonded to each other with piezoelectric actuator patches embedded. The nonlinear equations of motion for the laminated composite piezoelectric rectangular plate are derived from von Karman-type equation and third-order shear deformation plate theory of Reddy. The two-degree-of-freedom dimensionless equations of motion are obtained by using the Galerkin approach to the partial differential governing equation of motion for the laminated composite piezoelectric rectangular plate. The four-dimensional averaged equation in the case of primary parametric resonance and 1:3 internal resonances is obtained by using the method of multiple scales. From the averaged equation, the theory of normal form is used to find the explicit formulas of normal form. Based on the normal form obtained, the energy phase method is utilized to analyze the multi-pulse global bifurcations and chaotic dynamics for the laminated composite piezoelectric rectangular plate. The analysis of the global dynamics indicates that there exist multi-pulse jumping orbits in the perturbed phase space of the averaged equation. Based on the averaged equation obtained, the chaotic motions and the Shilnikov type multi-pulse orbits of the laminated composite piezoelectric rectangular plate are also found by numerical simulation. The results obtained above mean the existence of the chaos in the Smale horseshoe sense for the simply supported laminated composite piezoelectric rectangular plate.展开更多
基金Project(2014GK2013)supported by the Science and Technology Program of Hunan Province,China
文摘The microstructure evolution and properties of an Al-Zn-Mg-Cu alloy were investigated under different non-linear cooling processes from the solution temperature, combined with in-situ electrical resistivity measurements, selected area diffraction patterns (SADPs), transmission electron microscopy (TEM), and tensile tests. The relative resistivity was calculated to characterize the phase transformation of the experimental alloy during different cooling processes. The results show that at high temperatures, the microstructure evolutions change from the directional diffusion of Zn and Mg atoms to the precipitation of S phase, depending on the cooling rate. At medium temperatures, q phase nucleates on A13Zr dispersoids and grain boundaries under fast cooling conditions, while S phase precipitates under the slow cooling conditions. The strength and ductility of the aged alloy suffer a significant deterioration due to the heterogeneous precipitation in medium temperature range. At low temperatures, homogeneously nucleated GP zone, η′ and η phases precipitate.
基金Project(51104016)supported by the National Natural Science Foundation of ChinaProject(51925401)supported by the National Natural Science Foundation for Distinguished Young Scholars of ChinaProject(2019B10087)supported by Ningbo Science and Technology Innovation 2025 Major Project,China。
文摘A solid/liquid continuous casting and composite technology was used to produce d8.5 mm brass cladding pure copper stranded wire composite billet and the composite billet was then drawn. The results showed that the composite billet had good surface quality, metallurgical bonding interface between brass and pure copper as well as elongation of 53.1%. Synergistic deformation degree between pure copper wire and brass cladding layer was high during drawing. With an increase of the total deformation amount, the plastic deformation of the pure copper wire reduced triangular arc gaps between the pure copper wires and the triangular arc gaps were fully filled at 50%. When the total deformation amount was increased to 63%, dislocation cells and microbands successively formed in the pure copper wire. In the brass cladding layer, planar dislocation networks, twins and shear bands formed successively, and the main deformation mechanisms were dislocation sliding, twinning and shear deformation. The tensile strength increased from 240 MPa of the composite billet to 519 MPa of the one with the deformation amount of 63%, but the elongation decreased from 53.1% to 3.2%. A process of solid/liquid continuous casting and composite forming→drawing can work as a new compact method to produce brass cladding pure copper stranded wire composite as railway through grounding wire.
基金Project supported by the National Key Technology R &D Program(2006BAB01A07)
文摘Using the finite element method and Cole-Cole model for dual-frequency IP method to research numerical simulation, the authors introduced the fundamental principle of the dual-frequency IP method and the boundary value problem and variational equations, then replaced the complex resistivity of the model with the Cole-Cole model's parameters under ignoring the EM effect. Through solving the last linear equations, electric potentials of all the model's points were obtained. With changing model's parameters, the authors got different curves of the Fs and phases. According to the results of the simulation, the algorithm is proved to be correct and adaptable.
基金Shanghai Science and Technology Devel-opm ent Funds ( No.0 2 DZ15 0 0 1)
文摘This paper presented a registration method based on Fourier transform for multi-band images which is involved in translation and small rotation. Although different band images differ a lot in the intensity and features, they contain certain common information which we can exploit. A model was given that the multi-band images have linear correlations under the least-square sense. It is proved that the coefficients have no effect on the registration progress if two images have linear correlations. Finally, the steps of the registration method were proposed. The experiments show that the model is reasonable and the results are satisfying.
基金National Natural Science Foundation of China under Grant Nos.10472091,10332030,and 10502042the Natural Science Foundation of Shaanxi Province under Grant No.2003A03
文摘In this paper, we introduce a new invariant set Eo={u:ux=f'(x)F(u)+ε[g'(x)-f'(x)g(x)]F(u)×exp(-∫^u1/F(z)dz)}where f and g are some smooth functions of x, ε is a constant, and F is a smooth function to be determined. The invariant sets and exact sohltions to nonlinear diffusion equation ut = ( D(u)ux)x + Q(x, u)ux + P(x, u), are discussed. It is shown that there exist several classes of solutions to the equation that belong to the invariant set Eo.
文摘In this paper, the generator set of R 〈 x1,x2 〉G is obtained in according to the group G = Gl(n,R). The conditions of G = Gl(n, R) -equivalence of a pair of curves are found in terms of G = Gl(n, R)-invariants. And the independence of GL(n, R) -invariants is shown.
基金Project supported by the National Natural Science Foundation of China (Nos. 30570053 and 40501037)the National High Technology Research and Development Program (863 Program) of China (No. 2007AA10Z409)+1 种基金the National"Eleventh Five Years Plan" Key Project on Science and Technology of China (No. 2006BAJ08B01)the Research Fund of Science and Technology Bureau of Zhejiang Province,China (No. 2008C23088)
文摘The actinomycete populations and functions in cadmium (Cd) contaminated soil were investigated by the cultivation- independent molecular methods. The genomic DNA was extracted and purified from soil adulterated with various con- centrations of Cd in the laboratory. The partial 16S rDNA genes were amplified by polymerase chain reaction (PCR) using specific primers bound to evolutionarily conserved regions within these actinomycete genes. The diversity in PCR- amplified products, as measured by denaturing gradient gel electrophoresis (EGGE), was used as a genetic fingerprint of the population. Principle component analysis and Shannon-Weaver diversity index (H) analyses were used to analyze the DGGE results. Results showed that the two principal components accounted for only a low level of the total variance. The value H in contaminated soil was lower than that in the control at later stages of cultivation, whereas at earlier stages it was higher. Among the six sampling time points, the first, fifth and sixth weeks had the highest values of H. Significantly negative correlations between bioavallable Cd concentration and H values existed in the samples from weeks 2 (R = 0.929, P 〈 0.05) and 4 (R = 0.909, P 〈 0.05). These results may shed light on the effect of Cd on the soil environment and the chemical behavior and toxicity of Cd to actinomycetes.
基金supported by the National Natural Science Foundation of China under Grant No. 10671156the Program for New Century Excellent Talents in Universities under Grant No. NCET-04-0968
文摘New classes of exact solutions of the quasi-linear diffusion-reaction equations are obtained by seeking for the high-order conditional Lie-Baeklund symmetries of the considered equations. The method used here extends the approaches of derivative-dependent functional separation of variables and the invariant subspace. Behavior to some solutions such as blow-up and quenching is also described.
文摘In the period 2003-2011, lightning over-voltages accounted for about 47% of the total number of distribution transformer failures observed in the service area ofAES Sul, a power company that operates in the state of Rio Grande doSul, in South Brazil. This paper presents the results of an investigation on the influence of the distance between transformer and MV arresters on the surges at the transformer windings caused by direct strikes to the MV network. The analysis, performed through simulations using the Alternative Transients Program, shows that in general higher voltages are produced by subsequent strokes. Although in relation to the primary side the surges transferred to the secondary are much less affected by the distance between transformers and primary arresters, such distance should always be kept as short as possible in order to reduce the probability of occurrence of transformer failures due to over-voltages at the MV bushings.
基金Supported by Research Fond for the Doctoral of Higher Education of China,the Hunan Natural Science Foundation under Grant No.05JJ30121the Scientific Research Fund of Hunan Provincial Education Department under Grant No.08B011Educational Research Fund of Hunan Provincial Education Department under Grant No.09C013
文摘A new image encryption approach is proposed.First,a sort transformation based on nonlinear chaoticalgorithm is used to shuffle the positions of image pixels.Then the states of hyper-chaos are used to change the greyvalues of the shuffled image according to the changed chaotic values of the same position between the above nonlinearchaotic sequence and the sorted chaotic sequence.The experimental results demonstrate that the image encryptionscheme based on a shuffling map shows advantages of large key space and high-level security.Compared with someencryption algorithms,the suggested encryption scheme is more secure.
文摘The hot deformation behavior of Ti-6Al-4V (TC4) titanium alloy was investigated in the temperature range from 650℃ to 950℃ with the strain rate ranging from 7.7×10^-4 s^-1 to 7.7×10^-2 s^-1. The hot tension test results indicate that the flow stress decreases with increasing the deformation temperature and increases with increasing the strain rate. XRD analysis result reveals that only deformation temperature affects the phase constitution. The microstructure evolution under different deformation conditions was characterized by TEM observation. For the deformation of TC4 alloy, the work-hardening is dominant at low temperature, while the dynamic recovery and dynamic re-crystallization assisted softening is dominant at high temperature.
文摘With the increasingly widespread application of linear algebra theory, and in its opposite direction is not enough emphasis, linear algebra, several important points: matrix, determinant, linear equations, linear transformations, matrix keratosis and other anti-deepening understanding of the basics and improve the comprehensive ability to solve problems.
文摘The proof system, based on resolution method, has become quite popular in automatic theorem proving, because this method is simple to implement. At present many kinds of extensions for resolution method are known: Resolution with restricted number of variables in disjuncts, resolution over Linear Equations, Cutting planes, etc. For Classical, Intuitionistic and Minimal (Johansson's) propositional logics, the authors introduce the family of resolution systems with full substitution rule (SRC, SRI and SRM) and with e-restricted substitution rule (SeRC, SeRf and SeRM), where the number of substituted formula connectives is bounded by . The authors show that for each of mentioned logic the SR-type system (in tree form) is polynomially equivalent to Frege systems by size, but for every ~' 〉 0, Se+lR-type has exponential speed-up over the SeR-type (in tree form).
基金Project(08SK1002) supported by the Major Project of Science and Technology Department of Hunan Province,China
文摘In order to enhance forecasting precision of problems about nonlinear time series in a complex industry system,a new nonlinear fuzzy adaptive variable weight combined forecasting model was established by using conceptions of the relative error,the change tendency of the forecasted object,gray basic weight and adaptive control coefficient on the basis of the method of fuzzy variable weight.Based on Visual Basic 6.0 platform,a fuzzy adaptive variable weight combined forecasting and management system was developed.The application results reveal that the forecasting precisions from the new nonlinear combined forecasting model are higher than those of other single combined forecasting models and the combined forecasting and management system is very powerful tool for the required decision in complex industry system.
基金Project supported by the National Natural Science Foundation of China
文摘The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with "slow" decay initial data. By constructing an example, first it is illustrated that the classical solution to this kind of Cauchy problem may blow up in a finite time, even if the system is weakly linearly degenerate. Then some lower bounds of the life-span of classical solutions are given in the case that the system is weakly linearly degenerate. These estimates imply that, when the system is weakly linearly degenerate, the classical solution exists almost globally in time. Finally, it is proved that Theorems 1.1-1.3 in [2] are still valid for this kind of initial data.
基金the National Natural Science Foundation of China ( Grant No. 10272010) the Ministry of Science and Technology of China (Grant No. 2002CCC00200).
文摘Based on the test data of frictional materials and previous research achievements in this field, a generalized non-linear strength theory (GNST) is proposed. It describes non-linear strength properties on the π-plane and the meridian plane using a unified formula, and it includes almost all the present non-linear strength theories, which can be used in just one material. The shape of failure function of the GNST is a smooth curve between the SMP criterion and the Mises criterion on the π-plane, and an exponential curve on the meridian plane. Through the transformed stress space based on the GNST, the combination of the GNST and various constitutive models using p and q as stress parameters can be realized simply and rationally in three-dimensional stress state. Keywords generalized non-linear strength theory (GNST) - transformed stress - constitutive model - application
基金supported by National Institute on Drug Abuse(Grant Nos.R21-DA024260 and P50-DA10075)National Natural Science Foundation of China(Grant Nos.11071077,11371236,11028103,11071022 and 11028103)+2 种基金Innovation Program of Shanghai Municipal Education CommissionPujiang Project of Science and Technology Commission of Shanghai Municipality(Grant No.12PJ1403200)Program for New Century Excellent Talents,Ministry of Education of China(Grant No.NCET-12-0901)
文摘We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon- cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of o(√n), where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10872010, 10732020 and 11072008)the National Science Foundation for Distinguished Young Scholars of China (Grant No. 10425209)+1 种基金the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipalitythe Ph.D. Programs Foundation of Beijing University of Technology (Grant No. 52001015200701)
文摘The multi-pulse orbits and chaotic dynamics of a simply supported laminated composite piezoelectric rectangular plate under combined parametric excitation and transverse excitation are studied in detail. It is assumed that different layers are perfectly bonded to each other with piezoelectric actuator patches embedded. The nonlinear equations of motion for the laminated composite piezoelectric rectangular plate are derived from von Karman-type equation and third-order shear deformation plate theory of Reddy. The two-degree-of-freedom dimensionless equations of motion are obtained by using the Galerkin approach to the partial differential governing equation of motion for the laminated composite piezoelectric rectangular plate. The four-dimensional averaged equation in the case of primary parametric resonance and 1:3 internal resonances is obtained by using the method of multiple scales. From the averaged equation, the theory of normal form is used to find the explicit formulas of normal form. Based on the normal form obtained, the energy phase method is utilized to analyze the multi-pulse global bifurcations and chaotic dynamics for the laminated composite piezoelectric rectangular plate. The analysis of the global dynamics indicates that there exist multi-pulse jumping orbits in the perturbed phase space of the averaged equation. Based on the averaged equation obtained, the chaotic motions and the Shilnikov type multi-pulse orbits of the laminated composite piezoelectric rectangular plate are also found by numerical simulation. The results obtained above mean the existence of the chaos in the Smale horseshoe sense for the simply supported laminated composite piezoelectric rectangular plate.