ACADEMIC RESEARCH

Research Statement: [PDF]

Publication List: [PDF]                 

YANG LIU 

Publications

1. On the Schatten p-Quasi-Norm Minimization for Low-Rank Matrix Recovery, Authors: Yang Liu (刘洋), M. J. Lai, S. Li, and H. Wang, Applied and Computational Harmonic Analysis, Volume 51, pp 157-170, 2021.

2. Random Matrices and Compressed Sensing: Theory and Applications, Yang Liu (刘洋), ISBN: 979-8397369503, Science Press of Amazon, 2023

3. Exploring Gradient Descent: A Mathematical, Visual, and Coding Perspective, Int. J. Res. Publ. Rev., Vol 4, no 11, pp 3458-3466 October 2023 

4. A Mathematical Approach to Analyzing and Addressing Customer Service Inefficiencies in an International Company, World J. Adv. Eng. Technol. Sci., 2024, 11(02), 220–226 

5. On Mathematics For Explainable Machine Learning: Method And Applications, IJRES, Volume 12, PP. 26-37 (2023).

6. On the Decay of the Smallest Singular Value of Submatrices of Rectangular Matrices, [PDF], with Y. Wang, (23 pages), Asian-European Journal of Mathematics, World Scientific, DOI: 10.1142/S1793557116500753, Vol. 9, No. 3 (2016).

7. Promoting Fairness and Equality in Higher Education Administration: A Mathematical Perspective on Service Quality Control, Author: Yang Liu (刘洋), IJLSRA, 2024, 06(01), 129-136.

8. On Pedagogy on Leibniz's Rule and its Generalizations in Sobolev Spaces, Int. J. Res. Publ. Rev., Vol 4, no 11, pp 1231-1236, 2023 

9. Data-Driven Decisions: How Mathematics Shapes Business Strategy, Yang Liu (刘洋), ISBN: 979-8884578562, Science Press of Amazon, 2023.

10. On Application of Generalized Singular Value in Accuracy Analysis of Medical Image Classification, Authors: Yang Liu (刘洋), International Journal of Research Publication and Reviews, Volume 4, Issue 6, pp 2799-2806, 2023.

11. On the Surface Gravitational Acceleration of Mars, Authors: Yang Liu (刘 洋), WJAETS, 2022, 07(01), 169–173.

12. Generalization and Construction Beauties and Philosophy in Mathematics, Philosophy of Mathematics Education Journal,  2021, Issue 38, p1-8. 8p. 

13. Mathematical Models on Forest Logging and Carbon Sequestration, Authors: Yang Liu (刘洋) and Z. Huang, accepted for publication, Journal of Mathematics and Statistics Studies, Volume 4, No. 1, 36-53, 2023.

14. A Note on ell^{infty} Space in Integral Geometry,  IRJ-METS, Volume 5 Issue 11,  2023

15. On Concave Optimizations and generalized majorization on singular values of operators between Hilbert Spaces, preprint prepared, 2020.

16. Structure of Symmetry Group of Some Composite Links and Some Applications, Appl. Gen. Topol., Vol 21, No 2 (2020).

17. On the Kähler Form of Complex L^p Space and Its Lagrangian Subspaces, [PDF], DOI: 10.1007/s11868-015-0114-z, Journal of Pseudo-Differential Operators and Applications, Volume 6, Issue 2, pp 265-277, 2015.

18. On Crofton Measure and Its Applications in Geometry and Image Analysis, IRJMETS, Volume 05, Issue 11, 2023

19. Comparison on the Robustness Against Erasure of Numerically Erasure-robust Frames, Int. J. Appl. Math., Vol 21, No 2 (2020)

20. On the Surface Gravitational Acceleration of Mars, Authors: Yang Liu (刘 洋), WJAETS, 2022, 07(01), 169–173.

21. On the Representation Formula of Holmes-Thompson Areas, Differ. Geom.-Dyn. Syst., Vol.21, 2019, pp. 75-96, Volume 21 (2019)

22. The Probabilistic Estimates of the Largest Strictly Convex p-singular Value of Pregaussian Random Matrices, [PDF], DOI: 10.3844/jmssp.2015.7.15, Journal of Mathematics and Statistics, Volume 11, Issue 1, 2015, Pages 7-15.

23. On Structure Analysis of Finitely Generated Abelian Groups, Authors: Yang Liu (刘洋), World Journal of advanced Research and Reviews, 2022, 16(01), 923–927

24. On Earliest Deadline First Scheduling and Equality Before Deadline, Authors: Yang Liu (刘洋), Int. J. Trend Res. Dev., Volume 9 Issue 5, pp. 179-181, 2022.

25. On Low Rank Approximation of Linear Operators in p-Norms and Some Algorithms, [PDF], Asia-Pacific Journal of Operational Research, World Scientific, DOI: 10.1142/S0217595916500238, Vol. 33, No. 4 (2016).

26. Functional Decomposition of Ecological Networks by Probability Method, J. Math. Sci.: Adv. Appl., vol. 62, pp. 31-42, 2020.

27. On Geodesic Flow and Energy Functional on Riemannian Manifolds, Author: Yang Liu (刘洋), Pure and Applied Mathematics Journal, Vol. 10, No. 5, 2021, pp. 104-106.

28. Calculus Essentials and Applications: A Comprehensive Guide, published, 2023.

29. On Advising Students in Mathematical Research and Development, Authors: Yang Liu (刘洋), Int. J. Trend Res. Dev., Volume 9 Issue 4. pp. 215-216, 2022

30. The Probabilistic Estimates on the Largest and Smallest q-singular Values of Random Matrices, [PDF], with 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.

31. Random Matrices and Compressed Sensing: Theory and Applications, published, 2023.

32. The Null Space Property for Sparse Recovery from Multiple Measurement Vectors, [PDF], with M. J. Lai, DOI:10.1016/j.acha.2010.11.002, Applied and Computational Harmonic Analysis, Volume 30, Issue 3, 2011, Pages 402-406.

33. Algorithms for Generalized Lower Rank Approximations, submitted, 2013.

34. Two Results on the Schatten p-Quasi-Norm Minimization for Low-Rank Matrix Recovery, with M. J. Lai, S. Li and H. Wang, submitted for publication, 2012.

35. On the Lagrangian Subspaces of Complex Minkowski Space, [PDF], Journal of Mathematical Sciences: Advances and Applications, Volume 7, Number 2, 2011, Pages 87-93.

36. A New Estimate of Restricted Isometry Constant for Sparse Solutions, [PDF],with M. J. Lai, submitted for publication, 2011.

37. Non-convex Optimization for Linear System with Pregaussian Matrices and Recovery from Multiple Measurements, Ph.D. thesis, University of Georgia, 2010.

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

39. On Explicit Area Formula in Integral Geometry, accepted by Int. Math. Forum, 2011.

40. On the Range of Cosine Transform of Distributions for Torus-invariant Complex Minkowski Spaces, [PDF], arXiv:0910.5899, Far East Journal of Mathematical Sciences, Volume 39, Number 2, 2010, Pages 137-157.

41. Ropelength Under Linking Operation and Enzyme Action, General Mathematics, Volume 16, Number 1, 2008, Pages 55–58.

42. Exploring Integral: From Basics to Advanced Topics, Authors: Yang Liu (刘洋), ISBN: 979-8884174405, Higher Education of Amazon, 2023

Work in Preparation

• On Phase-shifting Fourier Algorithm and Phase Retrieval, with Y. Wang.

• On the ell_q Minimization Approach for Matrix Completion, with M. J. Lai.

• Lower Rank Approximation: A Generalization of Schmidt-Mirsky Theorem and Algorithms.

• On Aggregation Model of Marine Particles with QMOM, with A. Burd.

• On Feature Extractions in 3D Lung CT Image Deformation Registration, with D. Yang.

• Duality Theorems on Generalized Singular Values of Rectangular Matrices.

• On RIC and Singular Values of Rectangular Random Matrices, with M. J. Lai.

Research Related Professional Services

• Editorial Board Member(编委) for World Journal of Mathematics and Statistics

• Editorial Board Member(编委) 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(编委) 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 (刘洋), 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]