[1] H. Diao and H. Liu, Spectral Geometry and Inverse Scattering Theory, Springer, Cham, 2023, ISBN 9783031346156.
[2] H. Diao, R. Tang, and H. Liu, On quasi-Minnaert resonances in elasticity and their applications to stress concentrations, SIAM J. Appl. Math., to appear, 2026.
[3] H. Diao, Q. Meng, and Z. Sun, Effective medium theory for embedded sound-soft obstacles in an anisotropic inhomogeneous medium with applications, SIAM J. Appl. Math., to appear, 2026.
[4] H. Diao, X. Fei, and H. Liu, Geometrical characterizations of radiating and non-radiating elastic sources and mediums with applications, J. Differential Equations 463 (2026), 114208, 35 pp.
[5] H. Diao, H. Liu, and Q. Meng, Dislocations with corners in an elastic body with applications to fault detection, SIAM J. Appl. Math. 85 (2025), no. 5, 2399–2424.
[6] W. Zhou, H. Diao, and H. Liu, Quasi-Minnaert resonances in high-contrast acoustic structures and applications to invisibility cloaking, J. Comput. Phys. 541 (2025), 114310, 24 pp.
[7] H. Diao, Y. Geng, and R. Tang, Non-radiating elastic sources in inhomogeneous elastic media at corners with applications, Inverse Problems 41 (2025), no. 8, 085013, 27 pp.
[8] H. Diao, X. Fei, and H. Liu, On a novel unique continuation principle result and its application to inverse conductive scattering, SIAM J. Math. Anal. 57 (2025), no. 3, 3386–3421.
[9] H. Diao, H. Liu, Q. Meng, and L. Wang, On a coupled-physics transmission eigenvalue problem and its spectral properties with applications, J. Differential Equations 441 (2025), 113508, 39 pp.
[10] H. Diao, X. Fei, and H. Liu, Local geometric properties of conductive transmission eigenfunctions and applications, European J. Appl. Math. 36 (2025), no. 3, 538–569.
[11] H. Diao, X. Fei, H. Liu, and L. Wang, Determining anomalies in a semilinear elliptic equation by a minimal number of measurements, Inverse Problems 41 (2025), no. 5, 055004, 28 pp.
[12] H. Diao, H. Liu, Q. Meng, and L. Wang, Effective medium theory for embedded obstacles in electromagnetic scattering with applications, J. Differential Equations 437 (2025), 113283, 34 pp.
[13] H. Diao, R. Tang, H. Liu, and J. Tang, Unique determination by a single far-field measurement for an inverse elastic problem, Inverse Probl. Imaging 18 (2024), no. 6, 1405–1430.
[14] H. Diao, X. Fei, H. Liu, and K. Yang, Visibility, invisibility and unique recovery of inverse electromagnetic problems with conical singularities, Inverse Probl. Imaging 18 (2024), no. 3, 541–570.
[15] H. Diao, H. Liu, and L. Tao, Stable determination of an impedance obstacle by a single far-field measurement, Inverse Problems 40 (2024), no. 5, 055005, 35 pp.
[16] H. Diao, H. Li, H. Liu, and J. Tang, Spectral properties of an acoustic-elastic transmission eigenvalue problem with applications, J. Differential Equations 371 (2023), 629–659.
[17] H. Diao, X. Fei, H. Liu, and K. Yang, Visibility, invisibility and unique recovery of inverse electromagnetic problems with conical singularities, Inverse Probl. Imaging, doi:10.3934/ipi.2023043, 2023.
[18] Z. Bai, H. Diao, H. Liu, and Q. Meng, Stable determination of an elastic medium scatterer by a single far-field measurement and beyond, Calc. Var. Partial Differential Equations 61 (2022), 170, 23 pp.
[19] X. Cao, H. Diao, H. Liu, and J. Zou, Two single-measurement uniqueness results for inverse scattering problems within polyhedral geometries, Inverse Probl. Imaging 16 (2022), no. 6, 1501–1528.
[20] H. Diao, H. Liu, and L. Wang, Further results on generalized Holmgren’s principle to the Lamé operator and applications, J. Differential Equations 309 (2022), 841–882.
[21] Q. Meng, Z. Bai, H. Diao, and H. Liu, Effective medium theory for embedded obstacles in elasticity with applications to inverse problems, SIAM J. Appl. Math. 82 (2022), no. 2, 720–749.
[22] H. Diao, H. Liu, and B. Sun, On a local geometric structure of generalized elastic transmission eigenfunctions and application, Inverse Problems 37 (2021), 105015, 36 pp.
[23] X. Cao, H. Diao, H. Liu, and J. Zou, On novel geometric structures of Laplacian eigenfunctions in R3 and applications to inverse problems, SIAM J. Math. Anal. 53 (2021), no. 2, 1263–1294.
[24] H. Diao, H. Liu, L. Zhang, and J. Zou, Unique continuation from a generalized impedance edge-corner for Maxwell’s system and applications to inverse problems, Inverse Problems 37 (2021), 035004.
[25] Q. Meng, H. Diao, and Z. Bai, Condition numbers for the truncated total least squares problem and their estimations, Numer. Linear Algebra Appl. (2021), e2369.
[26] H. Diao, X. Cao, and H. Liu, On the geometric structures of conductive transmission eigenfunctions and their application, Comm. Partial Differential Equations 46 (2021), no. 4, 630–679.
[27] X. Cao, H. Diao, H. Liu, and J. Zou, On nodal and generalized singular structures of Laplacian eigenfunctions and applications, J. Math. Pures Appl. 143 (2020), 116–161.
[28] H. Diao, H. Liu, and L. Wang, On generalized Holmgren’s principle to the Lamé operator with applications to inverse elastic problems, Calc. Var. Partial Differential Equations 59 (2020), 179.
[29] Q. Meng, H. Diao, and Q. Yu, Structured condition number for multi-right hands linear systems with parameterized quasiseparable coefficient matrix, J. Comput. Appl. Math. 368 (2020), 112527.
[30] H. Diao, Z. Song, D. P. Woodruff, and X. Yang, Total least squares regression in input sparsity time, Adv. Neural Inf. Process. Syst. 32 (2019), 2478–2489.
[31] H. Diao, R. Jayaram, Z. Song, W. Sun, and D. P. Woodruff, Optimal sketching for Kronecker product regression and low rank approximation, Adv. Neural Inf. Process. Syst. 32 (2019), 4739–4750.
[32] H. Diao and Q. Meng, Structured generalized eigenvalue condition numbers for parameterized quasiseparable matrices, BIT 59 (2019), 695–720.
[33] H. Diao, P. Li, and X. Yuan, Inverse elastic surface scattering with far-field data, Inverse Probl. Imaging 13 (2019), no. 4, 721–744.
[34] H. Diao and Y. Sun, Mixed and componentwise condition numbers for a linear function of the solution of the total least squares problem, Linear Algebra Appl. 544 (2018), 1–29.
[35] H. Diao, Condition numbers for a linear function of the solution of the linear least squares problem with equality constraints, J. Comput. Appl. Math. 344 (2018), 640–656.
[36] H. Diao and J. Zhao, On structured componentwise condition numbers for Hamiltonian eigenvalue problems, J. Comput. Appl. Math. 335 (2018), 74–85.
[37] H. Diao, L. Liang, and S. Qiao, A condition analysis of the weighted linear least squares problem using dual norms, Linear Multilinear Algebra 66 (2018), no. 6, 1085–1103.
[38] H. Diao, Y. Wei, and P. Xie, Small sample statistical condition estimation for the total least squares problem, Numer. Algorithms 75 (2017), no. 2, 435–455.
[39] H. Diao, On condition numbers for least squares with quadric inequality constraint, Comput. Math. Appl. 73 (2017), no. 4, 616–627.
[40] H. Diao, Y. Wei, and S. Qiao, Structured condition numbers of structured Tikhonov regularization problem and their estimations, J. Comput. Appl. Math. 308 (2016), 276–300.
[41] H. Diao, X. Shi, and Y. Wei, Effective condition numbers and small sample statistical condition estimation for the generalized Sylvester equation, Sci. China Math. 56 (2013), no. 5, 967–982.
[42] H. Diao, W. Wang, Y. Wei, and S. Qiao, On condition numbers for Moore–Penrose inverse and linear least squares problem involving Kronecker products, Numer. Linear Algebra Appl. 20 (2013), no. 1, 44–59.
[43] H. Diao, H. Xiang, and Y. Wei, Mixed, componentwise condition numbers and small sample statistical condition estimation of Sylvester equations, Numer. Linear Algebra Appl. 19 (2012), no. 4, 639–654.
[44] H. Diao, On componentwise condition numbers for eigenvalue problems with structured matrices, Numer. Linear Algebra Appl. 16 (2009), 87–107.
[45] H. Diao and Y. Wei, On Frobenius normwise condition numbers for Moore–Penrose inverse and linear least squares problems, Numer. Linear Algebra Appl. 14 (2007), 603–610.
[46] F. Cucker and H. Diao, Mixed and componentwise condition numbers for rectangular structured matrices, Calcolo 44 (2007), 89–115.
[47] F. Cucker, H. Diao, and Y. Wei, On mixed and componentwise condition numbers for Moore–Penrose inverse and linear least squares problems, Math. Comp. 76 (2007), 947–963.
[48] F. Cucker, H. Diao, and Y. Wei, Smoothed analysis of some condition numbers, Numer. Linear Algebra Appl. 13 (2006), 71–84.
