By means of four different kinds of two-center expansions of the free-space Green function, the generalized scattered-wave molecular-orbital theory proposed by Johnson is resolved to approach the overlapping atomic-sp...By means of four different kinds of two-center expansions of the free-space Green function, the generalized scattered-wave molecular-orbital theory proposed by Johnson is resolved to approach the overlapping atomic-sphere MSW-X_α method. The improved result for the overlapping atomic-sphere is obtained to keep the computational advantages of the well-known nonoverlapping atomlc-sphere model without involving multicenter molecular integrals.展开更多
The present paper deals with the eigenvalues of complex nonlocal Sturm-Liouville boundary value problems.The bounds of the real and imaginary parts of eigenvalues for the nonlocal Sturm-Liouville differential equation...The present paper deals with the eigenvalues of complex nonlocal Sturm-Liouville boundary value problems.The bounds of the real and imaginary parts of eigenvalues for the nonlocal Sturm-Liouville differential equation involving complex nonlocal potential terms associated with nonlocal boundary conditions are obtained in terms of the integrable conditions of coefficients and the real part of the eigenvalues.展开更多
Aggregation equations are broadly used tomodel population dynamicswith nonlocal interactions,characterized by a potential in the equation.This paper considers the inverse problem of identifying the potential from a si...Aggregation equations are broadly used tomodel population dynamicswith nonlocal interactions,characterized by a potential in the equation.This paper considers the inverse problem of identifying the potential from a single noisy spatialtemporal process.The identification is challenging in the presence of noise due to the instability of numerical differentiation.We propose a robust model-based technique to identify the potential by minimizing a regularized data fidelity term,and regularization is taken as the total variation and the squared Laplacian.A split Bregman method is used to solve the regularized optimization problem.Our method is robust to noise by utilizing a Successively Denoised Differentiation technique.We consider additional constraints such as compact support and symmetry constraints to enhance the performance further.We also apply thismethod to identify time-varying potentials and identify the interaction kernel in an agent-based system.Various numerical examples in one and two dimensions are included to verify the effectiveness and robustness of the proposed method.展开更多
This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utiliz...This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.展开更多
文摘By means of four different kinds of two-center expansions of the free-space Green function, the generalized scattered-wave molecular-orbital theory proposed by Johnson is resolved to approach the overlapping atomic-sphere MSW-X_α method. The improved result for the overlapping atomic-sphere is obtained to keep the computational advantages of the well-known nonoverlapping atomlc-sphere model without involving multicenter molecular integrals.
基金Supported by the National Nature Science Foundation of China(12101356,12101357,12071254,11771253)the National Science Foundation of Shandong Province(ZR2021QA065,ZR2020QA009,ZR2021MA047)the China Postdoctoral Science Foundation(2019M662313)。
文摘The present paper deals with the eigenvalues of complex nonlocal Sturm-Liouville boundary value problems.The bounds of the real and imaginary parts of eigenvalues for the nonlocal Sturm-Liouville differential equation involving complex nonlocal potential terms associated with nonlocal boundary conditions are obtained in terms of the integrable conditions of coefficients and the real part of the eigenvalues.
基金supported in part by Simons Foundation grant 282311 and 584960supported in part by NSF grant NSF-DMS 1818751 and NSF-DMS 2012652+1 种基金supported in part by HKBU 162784 and 179356supported in part by NSF grants DMS-1522585 and DMS-CDS&E-MSS-1622453.
文摘Aggregation equations are broadly used tomodel population dynamicswith nonlocal interactions,characterized by a potential in the equation.This paper considers the inverse problem of identifying the potential from a single noisy spatialtemporal process.The identification is challenging in the presence of noise due to the instability of numerical differentiation.We propose a robust model-based technique to identify the potential by minimizing a regularized data fidelity term,and regularization is taken as the total variation and the squared Laplacian.A split Bregman method is used to solve the regularized optimization problem.Our method is robust to noise by utilizing a Successively Denoised Differentiation technique.We consider additional constraints such as compact support and symmetry constraints to enhance the performance further.We also apply thismethod to identify time-varying potentials and identify the interaction kernel in an agent-based system.Various numerical examples in one and two dimensions are included to verify the effectiveness and robustness of the proposed method.
文摘This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.
