 Prof. Alexander G. Ramm Department of Mathematics, Kansas State University, USA Research Interests: Differential and Integral Equations, Operator Theory, IllPosed and Inverse Problems, Mathematical Physics (Scattering Theory, Inverse Scattering, Wave Propagation), Functional Analysis And Spectral Theory, Applied Mathematics, Theoretical Numerical Analysis, Theoretical Electrical Engineering, Signal Estimation, Tomography

Alexander G. Ramm was born in Russia, emigrated to USA in 1979 and is a US citizen. He is Professor Emeritus of Mathematics with broad interests in analysis, scattering theory, inverse problems, theoretical physics, engineering, signal estimation, tomography, theoretical numerical analysis and applied mathematics. He is an author of 718 research papers, 20 research monographs and an editor of 3 books. He has lectured at many Universities throughout the world, gave more than 150 invited and plenary talks at various Conferences and had supervised 11 Ph.D students. He was Fulbright Research Professor in Israel and Ukraine; distinguished visiting professor in Mexico and Egypt; Mercator Professor in Germany; Research Professor in France; invited plenary speaker at the 7th PACOM; he won Khwarizmi international award in 2004 and received other honors. A.G.Ramm was the ﬁrst to prove uniqueness of the solution to inverse scattering problems with ﬁxedenergy scattering data; the ﬁrst to prove uniqueness of the solution to inverse scattering problems with nonoverdetermined scattering data and the ﬁrst to study inverse scattering problems with underdetermined scattering data. He studied inverse scattering problems for potential scattering and for scattering by obstacles. He solved many speciﬁc inverse problems and developed new methods and ideas in the area of inverse scattering problems. He introduced the notion of Property C for a pair of diﬀerential operators and applied Property C for onedimensional and multidimensional inverse scattering problems. A. G. Ramm solved manybody wave scattering problem when the bodies are small particles of arbitrary shapes, assuming that a much less than d and d is much less that λ, where a is the characteristic size of the particles, d is the minimal distance between neighboring particles, and λ is the wavelength in the material in which the small particles are embedded. Multiple scattering is essential under these assumptions. He used this theory to give a recipe for creating materials with a desired refraction coeﬃcient and materials with a desired wavefocusing property. These results attracted attention of the scientists working in nanotechnology. A. G. Ramm gave formulas for the scattering amplitude for scalar and electromagnetic waves by small bodies of arbitrary shapes and analytical formulas for the polarizability tensors for these bodies. A. G. Ramm gave a solution to the Pompeiu problem, proved the Schiﬀer’s conjecture and gave many results about symmetry problems for PDE, including ﬁrst symmetry results in harmonic analysis. A. G. Ramm has developed the Dynamical Systems Method (DSM) for solving linear and nonlinear operator equations, especially illposed. These results were used numerically and demonstrated practical eﬃciency of the DSM. A. G. Ramm developed random ﬁelds estimation theory for a wide class of random ﬁelds. A. G. Ramm has developed a theory of convolution equations with hypersingular integrals and solved analytically integral equations with hypersingular kernels. These results he applied to the study of the NSP (NavierStokes problem). As a result, he solved the millennium problem concerning the NavierStokes equations. A. G. Ramm formulated and proved the NSP paradox which shows the contradictory nature of the NSP and the nonexistence of its solution on all times for the initial data not identically equal to zero and the force equal to zero. A. G. Ramm has introduced a wide class of domains with noncompact boundaries. He studied the spectral properties of the Schr¨ odinger operators in this class of such domains and gave suﬃent conditions for the absence of eigenvalues on the continuous spectrum of these operators. A. G. Ramm developed the theory of local, pseudolocal and geometrical tomography. He has proved a variety of the results concerning singularities of the Radon transform and developed multidimensional algorithms for ﬁnding discontinuities of signals from noisy discrete data. Title: Solution of
the Millennium Problem on the NavierStokes Equations Abstract:
References 1. A. G. Ramm, The
NavierStokes problem, Morgan & Claypool Publish ers, 2021. 2. A. G. Ramm,
Theory of hypersingular integrals and its application to the NavierStokes
problem, Contrib. Math. 2, (2020), 4754. Open access Journal:
www.shahindp.com/locate/cm; DOI: 10.47443/cm.2020.0041 3. A. G. Ramm,
Comments on the NavierStokes problem, Axioms, 2021, 10, 95. Open
access Journal: https://www.mdpi.com/20751680/10/2 4. A. G. Ramm,
NavierStokes equations paradox, Reports on Math. Phys. (ROMP), 88, N1, (2021),
4145.  
 Prof. Yajun Liu South China University of Technology, China Research Interests: Digital signal processing technology and its application in mechanical systems (such as hydraulic System for Energy Saving.); Intelligence control and Manufacturing Engineering  Prof. Yajun Liu is a full professor in the Professor in the School of Mechanical and Automotive Engineering, South China University of Technology (2016at pressent). His research interests include Digital signal processing technology and its application in mechanical systems (such as hydraulic System for Energy Saving.); Intelligence control and Manufacturing Engineering. Moreover, Prof. Yajun Liu has published more than 150 papers in Journals and proceedings of international conferences. 35 patents on Mechanical System design and manufacturing.
 Prof. Grienggrai Rajchakit Faculty of Science, Maejo University Chiang Mai, Thailand Research Interests: Lyapunov methods,asymptotic stability,delays,timevarying systems,fuzzy control,linear matrix inequalities,neural nets,robust control,synchronisation,uncertain systems,closed loop systems,complex networks,control system synthesis,fuzzy
 G. Rajchakit was born in 1981. He received the B.S. degree in mathematics from Thammasat University, Bangkok, Thailand, in 2003, the M.S. degree in applied mathematics from Chiang Mai University, Chiang Mai, Thailand, in 2005, and the Ph.D. degree in applied mathematics from the King Mongkut’s University of Technology Thonburi, Bangkok, in the field of mathematics with specialized area of stability and control of neural networks. He is currently working as a Lecturer with the Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai. He has authored or coauthored more than 146 research articles in various SCI journals. His research interests include complexvalued NNs, complex dynamical networks, control theory, stability analysis, sampleddata control, multiagent systems, TS fuzzy theory, and cryptography. He was a recipient of the Thailand Frontier Author Award by the Thomson Reuters Web of Science in 2016 and the TRFOHECScopus Researcher Award by the Thailand Research Fund (TRF), Office of the Higher Education Commission (OHEC) and Scopus in 2016. He also serves as a reviewer for various SCI journals.(Based on document published on 24 February 2022).
 Prof. Oscar Eduardo Ruiz Salguero Universidad EAFIT, COLOMBIA Research Interests Computer Aided Geometric Design, Geometric Reasoning and Applied Computational Geometry
 Professor Oscar Ruiz was born in Tunja, Colombia. He obtained B.Sc. degrees in Mechanical Eng. (1983) and Computer Science (1987) at Los Andes University, Bogota, Colombia, a M.Sc. degree with emphasis in CAM (1991) and a Ph.D. with emphasis in CAD (1995) from the Mechanical & Industrial Eng. Dept. of University of Illinois at Urbana Champaign, USA. Dr. Ruiz has held Visiting Researcher positions at Ford Motor Co. (Dearborn, USA. 1993 and 1995), Fraunhofer Inst. Graphische Datenverarbeitung (Darsmstad, Germany 1999 and 2001), University of Vigo (1999 and 2002), Max Planck Institute for Informatik (2004) and Purdue University (2009). In 1996 Dr. Ruiz was appointed as Faculty of the Mechanical Eng. and Computer Science Depts. at EAFIT University, Medellin, Colombia, and has been ever since the Coordinator of the Laboratory for interdisciplinary Research on CAD / CAM / CAE. Dr. Ruiz’ interests are Computer Aided Geometric Design, Geometric Reasoning and Applied Computational Geometry.





