ACADEMIC RESEARCH

Research Statement: [PDF]

Publication List: [PDF]                 

YANG LIU 

Publications

1. On Matrix Analysis, Computation, and Its Applications, Author: Y. Liu*✉, 40+ pages, accepted for publication in an international journal, 2025 （SCI JCR Q1） 

 2. On the Schatten p-Quasi-Norm Minimization for Low-Rank Matrix Recovery, Authors: Y. Liu*, M. J. Lai, S. Li, and H. Wang, Applied and Computational Harmonic Analysis, Volume 51, Pages 157-170, 2021.(SCI JCR Q1) 

3. On Minimal Smallest Singular Value of Subframes for Signal Recovery, Author: Y. Liu*✉, Operators and Matrices, Volume 18, Number 2 (2024), 273–293.(SCI JCR Q3) 

4. Structure of Symmetry Group of Some Composite Links and Some Applications, Author: Y. Liu*✉, Appl. Gen. Topol., Vol 21, No 2 (2020) 

5. On the Representation Formula of Holmes-Thompson Areas, Author: Y. Liu*✉, Differ. Geom.-Dyn. Syst., Vol.21, 2019, pp. 75-96, Volume 21 (2019) 

6. Generalization and Construction: Beauties and Philosophy in Mathematics, Author: Y. Liu*✉, Philosophy of Mathematics Education Journal, Dec 2021, Issue 38, p1-8. 8p. 

7. On the Decay of the Smallest Singular Value of Submatrices of Rectangular Matrices, Authors: Y. Liu*✉, and Y. Wang, (23 pages), Asian-European Journal of Mathematics, World Scientific, DOI: 10.1142/S1793557116500753, Vol. 9, No. 3 (2016). 

8. Comparison on the Robustness Against Erasure of Numerically Erasure-robust Frames, Author: Y. Liu*✉, Int. J. Appl. Math., Vol 21, No 2 (2020). 

9. A Mathematical Approach to Analyzing and Addressing Customer Service Inefficiencies in an International Company, Authors: Y. Liu*✉, World Journal of Advanced Engineering and Technology Sciences, Volume 11, Issue 2, 2024, Pages 220–226. 

10. On Geodesic Flow and Energy Functional on Riemannian Manifold, Author: Y. Liu*✉, Pure Appl Math Journal, Vol. 10, No. 5, 2021, pp. 104-106. 

11. On Advising Students in Mathematical Research and Development, Author: Y. Liu*✉, Int. J. Trend Res. Dev., Volume 9, Issue 4, 2022. 

12. On the Kähler Form of Complex L^p Space and Its Lagrangian Subspaces, Author: Y. Liu*✉, Journal of Pseudo-Differential Operators and Applications, DOI: 10.1007/s11868-015-0114-z, Volume 6, Issue 2, pp 265-277, 2015.(SCI JCR) 

13. Low Rank Approximations of Linear Operators in p-norms and and Some Algorithms, Author: Y. Liu*✉, Asia-Pacific Journal of Operational Research, World Scientific, DOI: 10.1142/S0217595916500238, Vol. 33, No. 1 (2016) (SCI JCR) 

14. Functional Decomposition of Ecological Networks by Probability Method, Author: Y. Liu*✉, J. Math. Sci.: Adv. Appl., vol. 62, pp. 31-42, 2020. 

15. The Probabilistic Estimates of the Largest Strictly Convex p-singular Value of Pregaussian Random Matrices, Author: Y. Liu*✉, DOI: 10.3844/jmssp.2015.7.15, Journal of Mathematics and Statistics, Volume 11, Issue 1, 2015, Pages 7-15. 

16. On the Symmetry Group of a Type of Composite Link, Author: Y. Liu*✉, Applied Mathematical Sciences, indexed in SCImago, accepted for publication in 2018, Volume 13, 2019, Number 5, Pages 225 - 229. 

17. The Probabilistic Estimates on the Largest and Smallest q-singular Values of Random Matrices, Authors: Y. Liu*✉, and M. J. Lai, Article electronically published on October 30, 2014, Mathematics of Computation, S0025-5718(2014)02895-0, DOI: 10.1090/S0025-5718-2014-02895-0, Mathematics of Computation, Volume 84, Issue 294, 2015, Pages 1775-1794. (SCI JCR Q1) 

18. The Null Space Property for Sparse Recovery from Multiple Measurement Vectors, Authors: Y. Liu*✉, and M. J. Lai, DOI: 10.1016/j.acha.2010.11.002, Applied and Computational Harmonic Analysis, Volume 30, Issue 3, 2011, Pages 402-406.(SCI JCR Q1) 

19. On the Lagrangian Subspaces of Complex Minkowski Space, Author: Y. Liu*✉, Journal of Mathematical Sciences: Advances and Applications, Volume 7, Number 2, 2011, Pages 87-93. 

20. On Explicit Holmes-Thompson Area Formula in Integral Geometry, Author: Y. Liu*✉, accepted for publication, 2019. 

21. On the Range of Cosine Transform of Distributions for Torus-invariant Complex Minkowski Spaces, Author: Y. Liu*✉, Far East Journal of Mathematical Sciences, Volume 39, Number 2, 2010, Pages 137-157. 

22. Ropelength Under Linking Operation and Enzyme Action, Author: Y. Liu*✉, General Mathematics, Volume 16, Number 1, 2008, Pages 55-58. 

23. Developing a Dynamic Traffic Flow Model and Optimization Using Calculus Principles, Authors: Y. Liu*✉, International Journal of Research in Engineering and Science,  Volume 12, Issue 3, March 2024, Pages 389-406. 

24. Promoting Fairness and Equality in Higher Education Administration: A Mathematical Perspective on Service Quality Control, Author: Y. Liu*✉, IJLSRA, Volume 06, Issue 01, 2024, Pages 129-136. 

25. Mathematical Lens on Administrative Services, Authors: Y. Liu*✉, WJARR, Volume 21, Issue 3, 2024, Pages 1611–1616. 

26. Mathematical Models on Forest Logging and Carbon Sequestration, Authors: Y. Liu*✉, and Z. Huang, Journal of Mathematics and Statistics Studies, Volume 4, No. 1, 36-53. 

27. Exploring Gradient Descent: A Mathematical,  Visual, and Coding Perspective, Author: Y. Liu*✉, Int. J. Res. Publ. Rev., Vol 4, no 11, pp 3458-3466 October 2023 

28. A Note on ℓ^{\infty} Space in Integral Geometry, Author: Y. Liu*✉, IRJ-METS, Volume 5 Issue 11, 2023 

29. On Pedagogy on Leibniz's Rule and its Generalizations in Sobolev Spaces, Author: Y. Liu*✉, Int. J. Res. Publ. Rev., Vol 4, no 11, pp 1231-1236, 2023 

30. On Structure Analysis of Finitely Generated Abelian Groups, Authors: Y. Liu*✉, World Journal of advanced Research and Reviews, 16(01), 923–927 

31. On Earliest Deadline First Scheduling and Equality Before Deadline, Authors: Y. Liu*✉, Int. J. Trend Res. Dev., Volume 9 Issue 5, pp. 179-181 

32. On Mathematics For Explainable Machine Learning: Method And Applications, Authors: Y. Liu*✉, IJRES, Volume 12, PP. 26-37 

33. On Phase-shifting Fourier Algorithm and Phase Retrieval, Author: Y. Liu*✉, and Y. Wang, submitted. 

34. On Robustness Against Erasure Rate of NERF, Author: Y. Liu*✉, and Y. Wang, submitted. 

35. On Sufficient and Necessary Conditions for Recovery of Low-rank Matrices, Author: Y. Liu*✉, submitted. 

36. Lower Rank Approximation: A Generalization of Schmidt-Mirsky Theorem and Algorithms, Author: Y. Liu*✉, submitted. 

37. On Feature Extractions in 3D Lung CT Image Deformation Registration, Author: Y. Liu*✉, and D. Yang, submitted. 

38. On RIC and Singular Values of Rectangular Random Matrices, Author: Y. Liu*✉, and M. J. Lai, submitted. 

39. On EDF, FCFS, and Equality before Deadline, Author: Y. Liu, submitted, 2022. 

40. Randomness and Measurements, Author: Y. Liu, submitted to a top publisher. 

41. Two Results on the Schatten p-Quasi-Norm Minimization for Low-Rank Matrix Recovery, Authors: Y. Liu*✉, M. J. Lai, S. Li and H. Wang, submitted for publication, 2012. 

42. A New Estimate of Restricted Isometry Constant for Sparse Solutions, Authors: Y. Liu*✉, and M. J. Lai, submitted for publication, 2011. 

43. Duality on Generalized Singular Values, Their Analysis and Computations, Author: Y. Liu*✉, under review, JMAA, 2022. 

44. Generalized Concave Majorization of Singular Values of Operators on Hilbert Space, Author: Y. Liu*✉, under review, NLA, 2022. 

45. On Stability of Frames of Low Dimensions for Signal Processing, Author: Y. Liu*✉, under review, FMC, 2022. 

46. The Mathematical Foundations of Medicine: A Comprehensive Exploration, Author: Y. Liu*✉, Science Press of Amazon, ISBN: 979-8321773536, 2024. 

47. Mathematics of the Space Frontier: Navigating Mars Exploration, Author: Yang Liu*✉, Science of Amazon, ISBN: 979-8320815206, 2024. 

48. Mathematics of Justice: The Convergence of Abstract Reasoning and Legal Thought, Authors: Y. Liu*✉, Popular Science of Amazon, ISBN-13: 979-8320653273, 2024. 

49. The Symphony of Numbers: Unraveling the Mathematical Tapestry of Music, Author: Y. Liu*✉, Publisher: Science Press of Amazon, ISBN: 979-8321892749. 

50. The Foundations of Modern Civilization: A Mathematical Perspective, Author: Yang Liu*✉, Popular Science of Amazon, ISBN-13: 979-8320252377, 2024. 

51. Dynamics of the Social World: Modeling Change with Differential Equations, Author: Y. Liu*✉, Publisher: Science Press of Amazon, ISBN: 979-8320010113, 2024. 

52. The Calculus of Fairness: Exploring the Mathematics of Equal Opportunity, Author: Y. Liu*✉, Science of Amazon, ISBN-13: 979-8322689249, 2024. 

53. Exploring Integral: From Basics to Advanced Topics, Authors: Y. Liu*✉, ISBN: 979-8884174405, Higher Education of Amazon. 

54. Calculus Essentials and Applications: A Comprehensive Guide, Y. Liu*✉, ISBN-13: 979-8858439585, Higher Education of Amazon. 

55. Mathematics of the Earth: Quantitative Tales of Geological Time, Author: Y. Liu*✉, Science of Amazon, ISBN: 979-8320994871, 2024. 

56. Calculus of Administration: Mathematical Approaches to Organizational Efficiency, Author: Y. Liu*✉, Science Press of Amazon, ISBN-13: 979-8320030623, 2024. 

57. Data-Driven Decisions: How Mathematics Shapes Business Strategy, Y. Liu*✉, Science Press of Amazon, ISBN: 979-8884578562, 2024 

58. Random Matrices and Compressed Sensing: Theory and Applications, Y. Liu*✉, Science Press of Amazon, ISBN: 979-8397369503, 2023 

59. The Circle and the Square: Exploring the Mathematical Principles and Philosophies of Shape, Y. Liu*✉, Popular Science of Amazon, ISBN：979-8859458363, 2023 

60. Calculus Essentials and Applications: A Comprehensive Guide, Y. Liu*✉, Higher Education of Amazon. ISBN: 979-8858439585, 2023 

61. Majorization: From Classical Inequalities to Modern Optimization, Y. Liu*✉, Science of Amazon, ISBN：979-8883503831, 2023 

62. Lagrangian Subspaces of Manifolds, Author: Y. Liu*✉, InTech Press, ISBN 978-953-51-3132-8, 2017.  

63. On the Surface Gravitational Acceleration of Mars, Y. Liu*✉, WJETS, 2022, 07(01), 169–173. 

64. On Exactness and Splitting, Y. Liu*✉, WJARR, 2023, 20(02), 706–710.  

65. Mathematical Foundations of Artificial Intelligence: From Logic to Learning, Y. Liu*✉, Science of Amazon, ISBN: 979-8280314702, 2024 

66. Mathematics and the Architecture of Credibility: How Logical Structures and Quantitative Reasoning Build Trust in Knowledge and Systems, Y. Liu*✉, Science Press of Amazon, ISBN: 9798292225027, 2025

67. Algorithmic Justice: The Mathematical Foundations of Machine Learning in Law and Society, Y. Liu*✉, Science of Amazon, ISBN: 979-8280314702, 2025

68. Mathematical Foundations of Digital Shape: A Mathematical Guide to Geometric Modeling, Y. Liu*✉, Science Press of Amazon, ISBN: 979-8292183396, 2025

69. Mathematics of the Digital Economy: Models, Algorithms, and Applications, Author: Yang Liu*✉, Science Press of Amazon, ISBN: 979-8292556329, 2025 

Research Related Professional Services 

• Editorial Board Member for American Journal of Applied Mathematics

• Editorial Board Member for World Journal of Mathematics and Statistics

• Editorial Board Member for Annals of Applied Sciences

• Reviewer for Mathematical Reviews, AMS

• Judge for Conference Poster Presentations, MAA

• Journal Reviewer for Applied and Computational Harmonic Analysis

• Organizer for a special session of AMS Central Spring Sectional Meeting

• Editorial Board Member for Journal of Mathematical Research and Applications

• Journal Reviewer for Statistics and Probability Letters

• Journal Referee and Reviewer for Asia-Pacific Journal of Operational Research

• Journal Referee and Reviewer for IEEE/ACM Transactions on Computational Biology and Bioinformatics

• Journal Referee and Reviewer for American Journal of Applied Sciences

• Journal Referee and Reviewer for Appl. Math. J. Chinese Univ.

• Conference Proceedings Reviewer for 2015 International Conference on Mathematics and Computing

• Journal Referee and Reviewer for Int. J. Health Policy Manag.

• Journal Referee and Reviewer for KSII Transactions on Internet and Information Systems

• Journal Referee and Reviewer for Journal of Mathematical Research and Applications

Books and Book Projects

• Random Matrices and Compressed Sensing: Theory and Applications, published, 2023

• Calculus Essentials and Applications: A Comprehensive Guide, published, 2023

• The Circle and the Square: Exploring the Mathematical Principles and Philosophies of Shape，published, 2023

• Theories of Majorization and Minorization and Their Applications

• Mathematical Principle and Philosophy on "Round Outside but Square Inside"

• Book Chapter for Lagrangian Mechanics, published, ISBN 978-953-51-3132-8, 2017

• Exploring Integral: From Basics to Advanced Topics, Authors: Yang Liu, ISBN: 979-8884174405, Higher Education of Amazon, 2023

Selected Talks

• Non-convex Optimization for Linear System with Pregaussian Matrices and Recovery from Multiple Measurements (Slides [PDF])

• On the Aggregation Model of Marine Particles by Quadrature Method of Moments (Slides [PDF])

• On the Rauch Comparison Theorem and its Applications [PDF] (Slides [PDF])

• Aggregation Model of Marine Particles by Moments Method of Muilti-Modes (Slides [PDF])

Software

• • IHT for Recovery from Multiple Measurement Vectors, [RAR]