We study a nonlinear periodic problem driven by the p(t)-Laplacian and having a nonsmooth potential (hemivariational inequalities). Using a variational method based on nonsmooth critical point theory for locally L...We study a nonlinear periodic problem driven by the p(t)-Laplacian and having a nonsmooth potential (hemivariational inequalities). Using a variational method based on nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of at least two nontrivial solutions under the generalized subquadratic and then establish the existence of at least one nontrivial solution under the generalized superquadratic.展开更多
A fully discrete finite difference scheme for dissipative Zakharov equations is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions, the stability of the difference sche...A fully discrete finite difference scheme for dissipative Zakharov equations is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions, the stability of the difference scheme and the error bounds of optimal order of the difference solutions are obtained in L^2 × H^1 × H^2 over a finite time interval (0, T]. Finally, the existence of a global attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.展开更多
This note presents a set of new versions of Barbalat's lemma combining with positive (negative) definite functions.Based on these results,a set of new formulations of Lyapunov-like lemma are established.A simple ex...This note presents a set of new versions of Barbalat's lemma combining with positive (negative) definite functions.Based on these results,a set of new formulations of Lyapunov-like lemma are established.A simple example shows the usefulness of our results.展开更多
A stochastic logistic model with delays and impulsive perturbation is proposed and investigated. Sufficient conditions for extinction are established as well as nonpersistence in the mean, weak persistence and stochas...A stochastic logistic model with delays and impulsive perturbation is proposed and investigated. Sufficient conditions for extinction are established as well as nonpersistence in the mean, weak persistence and stochastic permanence. The threshold between weak persistence and extinction is obtained. Furthermore, the theoretical analysis results are also derivated with the help of numerical simulations.展开更多
A Jeffcott rotor-magnetic bearing with time delays is investigated in this paper. Firstly, it is found that the characteristic equation of the system satisfies the conditions of the singularity. Secondly, the center m...A Jeffcott rotor-magnetic bearing with time delays is investigated in this paper. Firstly, it is found that the characteristic equation of the system satisfies the conditions of the singularity. Secondly, the center manifold reduction and normal form are employed to study the bifurcation from simple zero and zero-purely imaginary singularities. The results of this paper will help to understand the influence of the time delays in feedback loop on the dynamics of rotor-magnetic bearing system.展开更多
In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibi...In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.展开更多
The stability and bifurcation of the trivial solution in the two_dimensional differential equation of a model describing human respiratory system with time delay were investigated. Formulas about the stability of bifu...The stability and bifurcation of the trivial solution in the two_dimensional differential equation of a model describing human respiratory system with time delay were investigated. Formulas about the stability of bifurcating periodic solution and the direction of Hopf bifurcation were exhibited by applying the normal form theory and the center manifold theorem.Furthermore,numerical simulation was carried out.展开更多
Stress concentration zones and the maximum value of thermal stress of TiC cermet/iron joint brazed with Ag-Cu-Zn filler metal during cooling were studied. The results show that when the temperature is 300K, the maxi...Stress concentration zones and the maximum value of thermal stress of TiC cermet/iron joint brazed with Ag-Cu-Zn filler metal during cooling were studied. The results show that when the temperature is 300K, the maximum values of shear stress and tensile stress on TiC cermet/iron interface both appear on the tip of Ag-Cu-Zn/iron interface, which makes Ag-Cu-Zn/iron interface become weak zone of the interface. Tensile stress on iron undersurface relaxes to the inner of iron, and the compression stress on iron undersurface concentrates on the side of iron as the temperature decreases, so cracks appear easily at the site where tensile and compression stress cross.展开更多
The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results a...The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results are essential generalizations of continuous dependence of bounded variation solutions on parameters for Kurzweil equations.展开更多
Remote sensing products are significant in the data assimilation of an ocean model. Considering the resolution and space coverage of different remote sensing data, two types of sea surface height(SSH) product are em...Remote sensing products are significant in the data assimilation of an ocean model. Considering the resolution and space coverage of different remote sensing data, two types of sea surface height(SSH) product are employed in the assimilation, including the gridded products from AVISO and the original along-track observations used in the generation. To explore their impact on the assimilation results, an experiment focus on the South China Sea(SCS) is conducted based on the Regional Ocean Modeling System(ROMS) and the four-dimensional variational data assimilation(4 DVAR) technology. The comparison with EN4 data set and Argo profile indicates that, the along-track SSH assimilation result presents to be more accurate than the gridded SSH assimilation, because some noises may have been introduced in the merging process. Moreover, the mesoscale eddy detection capability of the assimilation results is analyzed by a vector geometry–based algorithm. It is verified that, the assimilation of the gridded SSH shows superiority in describing the eddy's characteristics, since the complete structure of the ocean surface has been reconstructed by the original data merging.展开更多
A new widly convergent method for solving the problem of operator identification is illustrated. Numerical simulations are carried out to test the feasibility and to study the general characteristics of the technique ...A new widly convergent method for solving the problem of operator identification is illustrated. Numerical simulations are carried out to test the feasibility and to study the general characteristics of the technique without the real measurement data. This technique is a direct application of the continuation homo-topy method for solving nonlinear systems of equations. It is found that this method does give excellent results in solving the inverse problem of the elliptic differential equations.展开更多
In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Dis...In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Distributions, Engineering Decisions, Resource Allocations and other field of mathematical economics and engineering problems. Under the suitable assumption, it is proved to globally converge to a weak efficient solution of (MOP), if its x-branch has no weak infinite solution.展开更多
Based on information entropy theory, the definition of relative entropy, and the relative entropy minimum principle, this study establishes a multi-objective optimization model for a key valve opening of an urban wate...Based on information entropy theory, the definition of relative entropy, and the relative entropy minimum principle, this study establishes a multi-objective optimization model for a key valve opening of an urban water distribution network(WDN). Each node pressure is taken as the main research object to reduce pipeline leakage. Moreover, genetic algorithm is applied in the proposed model to solve the key valve opening of the actual WDN in a city in southern China. Using the proposed model, the relevant decision variables of a WDN can be optimized to provide a new manner of network dispatching.展开更多
The periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi_linear differential inclusion.Also existence theorem of the extr...The periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi_linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given for this class of semi_linear differential inclusion. An application to some feedback control systems is discussed.展开更多
This paper is concerned with estimation of electrical conductivity in Maxwell equations. The primary difficulty lies in the presence of numerous local minima in the objective functional. A wavelet multiscale method is...This paper is concerned with estimation of electrical conductivity in Maxwell equations. The primary difficulty lies in the presence of numerous local minima in the objective functional. A wavelet multiscale method is introduced and applied to the inversion of Maxwell equations. The inverse problem is decomposed into multiple scales with wavelet transform, and hence the original problem is reformulated to a set of sub-inverse problems corresponding to different scales, which can be solved successively according to the size of scale from the shortest to the longest. The stable and fast regularized Gauss-Newton method is applied to each scale. Numerical results show that the proposed method is effective, especially in terms of wide convergence, computational efficiency and precision.展开更多
For calculating the stiffness function of a structure, the differential equation of the vibration of the structure was divided into the differential equation on the original stiffness function that was known, and Fred...For calculating the stiffness function of a structure, the differential equation of the vibration of the structure was divided into the differential equation on the original stiffness function that was known, and Fredholm integral equation of the first kind on the undetermined stiffness function that was unknown. And the stable solutions of the integral equation, when the smooth factor was equal to zero, was solved by the extrapolation with p smooth factors. So the stiffness function of the structure is obtained. Applied examples show that the method is feasible and effective.展开更多
A numerical iterative model was derived from the difference method and a perturbation assumption to calculate the coefficient function of a wave equation. The method was used to solve the disaccord problem of numerica...A numerical iterative model was derived from the difference method and a perturbation assumption to calculate the coefficient function of a wave equation. The method was used to solve the disaccord problem of numerical precision between the direct problem model and inverse problem model, and its serial problems using the old method. Numerical simulation calculation shows that the method is feasible and effective.展开更多
The mechanism for the effects of pressure on the magnetic properties and the martensitic transformation of Ni-Mn- Sn shape memory alloys is revealed by first-principles calculations. It is found that the total energy ...The mechanism for the effects of pressure on the magnetic properties and the martensitic transformation of Ni-Mn- Sn shape memory alloys is revealed by first-principles calculations. It is found that the total energy difference between paramagnetic and ferromagnetic austenite states plays an important role in the magnetic transition of Ni-Mn-Sn under pressure. The pressure increases the relative stability of the martensite with respect to the anstenite, leading to an increase of the martensitic transformation temperature. Moreover, the effects of pressure on the magnetic properties and the martensitic transformation are discussed based on the electronic structure.展开更多
An adaptive multi-scale conjugate gradient method for distributed parameter estimations (or inverse problems) of wave equation is presented. The identification of the coefficients of wave equations in two dimensions i...An adaptive multi-scale conjugate gradient method for distributed parameter estimations (or inverse problems) of wave equation is presented. The identification of the coefficients of wave equations in two dimensions is considered. First, the conjugate gradient method for optimization is adopted to solve the inverse problems. Second,the idea of multi-scale inversion and the necessary conditions that the optimal solution should be the fixed point of multi-scale inversion method isconsidered. An adaptive multi-scale inversion method for the inverse problem is developed in conjunction with the conjugate gradient method. Finally, some numerical results are shown to indicate the robustness and effectiveness of our method.展开更多
基金supported by the National Science Foundation of China (11001063, 10971043)the Fundamental Research Funds for the Central Universities (HEUCF 20111134)+2 种基金China Postdoctoral Science Foundation Funded Project (20110491032)Heilongjiang Provincial Science Foundation for Distinguished Young Scholars (JC200810)Program of Excellent Team in Harbin Institute of Technology and the Natural Science Foundation of Heilongjiang Province (A200803)
文摘We study a nonlinear periodic problem driven by the p(t)-Laplacian and having a nonsmooth potential (hemivariational inequalities). Using a variational method based on nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of at least two nontrivial solutions under the generalized subquadratic and then establish the existence of at least one nontrivial solution under the generalized superquadratic.
基金Supported by the National Natural Science Foundation of China(10371077)
文摘A fully discrete finite difference scheme for dissipative Zakharov equations is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions, the stability of the difference scheme and the error bounds of optimal order of the difference solutions are obtained in L^2 × H^1 × H^2 over a finite time interval (0, T]. Finally, the existence of a global attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.
基金supported by National Natural Science Foundation of China(No.60710002,60974044)Program for Changjiang Scholars and Innovative Research Team in University
文摘This note presents a set of new versions of Barbalat's lemma combining with positive (negative) definite functions.Based on these results,a set of new formulations of Lyapunov-like lemma are established.A simple example shows the usefulness of our results.
基金supported by the National Natural Science Foundation of China(11271101)the NNSF of Shandong Province(ZR2010AQ021)
文摘A stochastic logistic model with delays and impulsive perturbation is proposed and investigated. Sufficient conditions for extinction are established as well as nonpersistence in the mean, weak persistence and stochastic permanence. The threshold between weak persistence and extinction is obtained. Furthermore, the theoretical analysis results are also derivated with the help of numerical simulations.
基金Supported by the Heilongjiang Province Department of Education Science and Technology Project (11544048)
文摘A Jeffcott rotor-magnetic bearing with time delays is investigated in this paper. Firstly, it is found that the characteristic equation of the system satisfies the conditions of the singularity. Secondly, the center manifold reduction and normal form are employed to study the bifurcation from simple zero and zero-purely imaginary singularities. The results of this paper will help to understand the influence of the time delays in feedback loop on the dynamics of rotor-magnetic bearing system.
基金the National Natural Science Foundation of China(No.40774056)Program of Excellent Team in Harbin Institute of Technology
文摘In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.
文摘The stability and bifurcation of the trivial solution in the two_dimensional differential equation of a model describing human respiratory system with time delay were investigated. Formulas about the stability of bifurcating periodic solution and the direction of Hopf bifurcation were exhibited by applying the normal form theory and the center manifold theorem.Furthermore,numerical simulation was carried out.
文摘Stress concentration zones and the maximum value of thermal stress of TiC cermet/iron joint brazed with Ag-Cu-Zn filler metal during cooling were studied. The results show that when the temperature is 300K, the maximum values of shear stress and tensile stress on TiC cermet/iron interface both appear on the tip of Ag-Cu-Zn/iron interface, which makes Ag-Cu-Zn/iron interface become weak zone of the interface. Tensile stress on iron undersurface relaxes to the inner of iron, and the compression stress on iron undersurface concentrates on the side of iron as the temperature decreases, so cracks appear easily at the site where tensile and compression stress cross.
基金The NSF (10271095) of China and NWNU-KJCXGC-212.
文摘The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results are essential generalizations of continuous dependence of bounded variation solutions on parameters for Kurzweil equations.
基金The National Key Research and Development Program of China under contract No.2016YFC1401800the National Natural Science Foundation of China under contract Nos 41576176 and 11401140the Key Project of Science and Technology of Harbin Institute of Technology at Weihai of China under contract No.2014 DXGJ14
文摘Remote sensing products are significant in the data assimilation of an ocean model. Considering the resolution and space coverage of different remote sensing data, two types of sea surface height(SSH) product are employed in the assimilation, including the gridded products from AVISO and the original along-track observations used in the generation. To explore their impact on the assimilation results, an experiment focus on the South China Sea(SCS) is conducted based on the Regional Ocean Modeling System(ROMS) and the four-dimensional variational data assimilation(4 DVAR) technology. The comparison with EN4 data set and Argo profile indicates that, the along-track SSH assimilation result presents to be more accurate than the gridded SSH assimilation, because some noises may have been introduced in the merging process. Moreover, the mesoscale eddy detection capability of the assimilation results is analyzed by a vector geometry–based algorithm. It is verified that, the assimilation of the gridded SSH shows superiority in describing the eddy's characteristics, since the complete structure of the ocean surface has been reconstructed by the original data merging.
文摘A new widly convergent method for solving the problem of operator identification is illustrated. Numerical simulations are carried out to test the feasibility and to study the general characteristics of the technique without the real measurement data. This technique is a direct application of the continuation homo-topy method for solving nonlinear systems of equations. It is found that this method does give excellent results in solving the inverse problem of the elliptic differential equations.
文摘In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Distributions, Engineering Decisions, Resource Allocations and other field of mathematical economics and engineering problems. Under the suitable assumption, it is proved to globally converge to a weak efficient solution of (MOP), if its x-branch has no weak infinite solution.
基金supported by the National Natural Science Foundation of China (No. 51178141)National Major Science and Technology Program for Water Pollution Control and Treatment (2012ZX07408-002-004-002)
文摘Based on information entropy theory, the definition of relative entropy, and the relative entropy minimum principle, this study establishes a multi-objective optimization model for a key valve opening of an urban water distribution network(WDN). Each node pressure is taken as the main research object to reduce pipeline leakage. Moreover, genetic algorithm is applied in the proposed model to solve the key valve opening of the actual WDN in a city in southern China. Using the proposed model, the relevant decision variables of a WDN can be optimized to provide a new manner of network dispatching.
文摘The periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi_linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given for this class of semi_linear differential inclusion. An application to some feedback control systems is discussed.
基金supported by the Program of Excellent Team of Harbin Institute of Technology
文摘This paper is concerned with estimation of electrical conductivity in Maxwell equations. The primary difficulty lies in the presence of numerous local minima in the objective functional. A wavelet multiscale method is introduced and applied to the inversion of Maxwell equations. The inverse problem is decomposed into multiple scales with wavelet transform, and hence the original problem is reformulated to a set of sub-inverse problems corresponding to different scales, which can be solved successively according to the size of scale from the shortest to the longest. The stable and fast regularized Gauss-Newton method is applied to each scale. Numerical results show that the proposed method is effective, especially in terms of wide convergence, computational efficiency and precision.
文摘For calculating the stiffness function of a structure, the differential equation of the vibration of the structure was divided into the differential equation on the original stiffness function that was known, and Fredholm integral equation of the first kind on the undetermined stiffness function that was unknown. And the stable solutions of the integral equation, when the smooth factor was equal to zero, was solved by the extrapolation with p smooth factors. So the stiffness function of the structure is obtained. Applied examples show that the method is feasible and effective.
文摘A numerical iterative model was derived from the difference method and a perturbation assumption to calculate the coefficient function of a wave equation. The method was used to solve the disaccord problem of numerical precision between the direct problem model and inverse problem model, and its serial problems using the old method. Numerical simulation calculation shows that the method is feasible and effective.
基金Project supported by the New Century Excellent Talents in Heilongjiang Provincial University,China(Grant No.1253-NCET-009)the Youth Academic Backbone in Heilongjiang Provincial University,China(Grant No.1251G022)the National Natural Science Foundation of China(Grant Nos.50901026 and 51301054)
文摘The mechanism for the effects of pressure on the magnetic properties and the martensitic transformation of Ni-Mn- Sn shape memory alloys is revealed by first-principles calculations. It is found that the total energy difference between paramagnetic and ferromagnetic austenite states plays an important role in the magnetic transition of Ni-Mn-Sn under pressure. The pressure increases the relative stability of the martensite with respect to the anstenite, leading to an increase of the martensitic transformation temperature. Moreover, the effects of pressure on the magnetic properties and the martensitic transformation are discussed based on the electronic structure.
文摘An adaptive multi-scale conjugate gradient method for distributed parameter estimations (or inverse problems) of wave equation is presented. The identification of the coefficients of wave equations in two dimensions is considered. First, the conjugate gradient method for optimization is adopted to solve the inverse problems. Second,the idea of multi-scale inversion and the necessary conditions that the optimal solution should be the fixed point of multi-scale inversion method isconsidered. An adaptive multi-scale inversion method for the inverse problem is developed in conjunction with the conjugate gradient method. Finally, some numerical results are shown to indicate the robustness and effectiveness of our method.