XINGPING SUN — Research Profile

XINGPING SUN — Research Proﬁle

AWARDS AND GRANTS 1. National Science Foundation: Research Experience for Undergraduate Students, with L. Reid, J. Rebaza, and S. Senger, $297,000 (2016-2018) . 2. The S˜aoPaulo Research Foundation and ENAMA, $2,896, (2014). 3. National Science Foundation: Research Experience for Undergraduate Students, with L. Reid and J. Rebaza, $297,000 (2012-2014) . 4. Missouri State University Faculty Summer Research Fellowship Award, $6,000 (2011). 5. Summer Visiting Fellowship Award, $4,928, Fudan University, Shanghai, China, (2010). 6. Visiting Fellowship Research Grant, with J. Levesley and W. Castell, $8,750 Engineering and Physical Sciences Research Council of Great Britain, (2009). 7. Summer Visiting Fellowship Award, $4,928, Fudan University, Shanghai, China, (2007). 8. Excellence in Teaching Award, $1,200, College of Natural and Applied Sciences, Missouri State University, (2006). 9. Missouri State University Excellence in Research Award, $2,400 (2004). 10. Missouri State University Faculty Research Grant, $3,575 (2004). 11. Missouri State University Faculty Summer Research Fellowship Award, $5,000 (2004). 12. Visiting Fellowship Research Grant, $15,240 Engineering and Physical Sciences Research Council of Great Britain, (2003-2005). 13. Missouri State University Faculty Summer Research Fellowship Award, $5,000 (2000). 14. Missouri State University Faculty Research Grant, $5,500 (1999). 15. Missouri State University Faculty Summer Research Fellowship Award, $ 5,000 (1997). 16. Missouri State University Foundation Excellence in Research Award, $2,400 (1996) 17. Visiting Fellowship Research Grant, $2,240 Engineering and Physical Sciences Research Council of Great Britain, (1995). 18. Visiting Fellowship Research Grant, The S˜aoPaulo Research Foundation, $5,500 (1994). 19. Missouri State University Faculty Summer Research Fellowship Award, $4,000 (1994). 20. Visiting Fellowship Research Grant, $4,640 Science and Engineering Research Council of Great Britain, (1993).

PUBLICATIONS ( 2003 - 2015 all peer-reviewed) —∗ indicates work with students: 1. Theory and applications of positive deﬁnite functions, monograph, 2014. 2. ∗ The existence of limit and continuity, with Julie Millett, to appear in College Mathematical Journal. 3. ∗ Convergence of Sequences of Polygons, with Eric Hintikka, to appear in Involve - a Journal of Mathematics.

1 4. Interpolation of functions of exponential type by shifts of a basis function, with A. Kushpel and J. Levesley, submitted. 5. A general type of spherical mean operators and K-functionals of fractional orders, with T. Jordao, Communication in Pure and Applied Analysis 14, No. 3 (2015), 743-757. 6. Eigenvalue sequences of positive integral operators and moduli of smoothness, with T. Jordao and V. Menegatto, in “Approximation Theory XIV: San Antonio 2013”, 239-254, G. E. Fasshauer and L.L. Schumaker (eds). 7. Discretizing Spherical Integrals and Its Applications, with S. Lin and Z. Xu, in “Dynamical Systems, Diﬀerential Equations and Applications, Discrete and Continuous Dynamic Systems- Proceedings 2013, 499 - 514, D. Costa, W. Feng, Z. Feng, X. Lu, X. Sun, M. Taniguchi, and A. Vitola (eds), AIMS Publication. 8. Learning capability of relaxed greedy algorithms, with S. Lin, Y. Rong, and Z. Xu, IEEE Transactions on Neural Networks and Learning Systems 24 (2013), 1598-1608. 9. Sampling scattered data with Bernstein polynomials: stochastic and deterministic error estimates, with Z. Wu and L. Ma, Advances in Computational Mathematics 38 (2013), no. 1, 187-205.

10. Kernel Approximation on Manifolds II: The L∞-norm of the L2-projector, with T. Hangel- broek, F. Narcowich, and J. Ward, SIAM Journal on Mathematical Analysis 43 (2011), No. 2, 662-684. 11. Approximating probability measures on manifolds via radial basis functions, with J. Levesley, Book Chapter, in “Approximation Algorithms for Complex Systems”, E. Georgoulis, A. Iske and J. Levesley, (eds.), Springer-Verlag, Berlin, Heidelberg, 151-180, 2011. 12. LeVeque type inequalities and discrepancy estimates for minimal energy conﬁgurations on spheres, with F. Narcowich, J. D. Ward, and Z. Wu, Journal of Approximation Theory 162 (2010), no. 6, 1256–1278.

13. Approximation on the Voronoi cells of the Ad lattice, Constructive Approximation 32 (2010), 543–567. 14. Energy estimates and invariant groups on compact homogeneous manifolds, with S. Damelin, J. Levesley, and D. Ragozin, Journal of Complexity 25 (2009), 152-162. 15. Spherical basis functions and uniform distribution of points on spheres, with Z. Chen, Journal of Approximation Theory 151 (2008), 186-207. 16. Energy estimates and the Weyl Criterion on compact homogeneous manifolds, with S. Damelin and J. Levesley, in “Algorithms for Approximation V”, A. Iske and J. Levesley, (eds.), Springer-Verlag, Heidelberg, 359–367, 2007. 17. Direct and inverse Sobolev error estimates for scattered data interpolation via spherical basis functions, with F. Narcowich, J. D. Ward, and H. Wendland, Foundation of Computational Mathematics 7 (2007), no. 3, 369–390. 18. Minimal discrete energy and discrepancy on spheres, with A.B.J. Kuijlaars and E. B. Saﬀ, Journal of Computational and Applied Mathematics 199 (2007), no. 1, 172–180. 19. Approximation in Sobolev spaces on spherical domains, with F. Narcowich and J. D. Ward, Advances in Computational Mathematics 27 (2007), no. 1, 107–124.

2 20. Perturbation of operators associated with interpolations on manifolds, with J. Levesley, Jour- nal of Computational and Applied Mathematics 199 (2007), no. 1, 159–171. 21. Corrigendum to and two open questions arising from “Approximation in rough native spaces by shifts of smooth kernels on spheres”, with J. Levesley, Journal of Approximation Theory 138 (2006), 124-127. 22. Approximation in rough native spaces by shifts of smooth kernels on spheres, with J. Levesley, J. Approximation Theory 133 (2005), 269-283. 23. Strictly positive definite functions on the unit circle, Mathematics of Computation 74 (2005), 709-721. 24. A necessary and sufficient condition for strictly positive definite functions on spheres, with D. Chen and V. Menegatto, The Proceedings of American Mathematical Society 131 (2003), 2733-2740.

MASTER’S THESES AND SEMINAR PAPERS DIRECTED 1. Solving Partial diﬀerential equations on various domains, (Thesis) by Ibranheem Otuf, ex- pected completion Spring 2016. 2. Bernstein polynomials and their applications in computer aided geometric designs, (Thesis) by Cody Lawson, completed in 2012. 3. The Gauge integral and its connection to Lebesgue integral, (Thesis) by Andrew Swift, completed in 2011. 4. An introduction to uniform distribution modulo one, (Thesis) by Stacy Robinson, completed in 2011. 5. Convergence and Lebesgue integrals in analysis, (Thesis) by Ryan Thomas, completed in 2009. 6. Topological Properties and their relations, (Thesis) by Suchitra Sripada, completed in 2006. 7. Cardinality and countability, (Seminar paper) by Terry Wright Jr., completed in 2006. 8. Existence of limit and continuity, (Thesis) by Julie Millett, completed in 1993. 9. On various convergence problems in analysis, (Seminar paper) by Gary Boyd, completed in 1993.

SELECT INVITED TALKS 1. The solvability of radial basis function interpolation, in “The Sixth Texas International Sym- posium on Approximation Theory”, College Station, TX, 1989. 2. Ridge functions and their application in multivariate interpolation, in “UT and Texas A&M Joint Conference on Approximation Theory”, Center for Approximation Theory, Texas A&M University, 1989. 3. Interpolation by sums of ridge functions, Seminar, Center for Approximation Theory, Texas A&M University, 1989. 4. Multivariate interpolation using linear combinations of radial basis functions, in “The Sixth Conference of Southeast Approximators”, Memphis State University, 1991.

3 5. Ridge function spaces and their interpolation property, in “The Seventh Texas International Symposium on Approximation Theory”, Austin, Texas, 1992. 6. Analytic monotone extensions, in “The 873rd Regional Conference of American Mathematical Society”, Springfield, MO, 1992. 7. Scattered Hermite interpolation by positive definite functions, Seminar, Department of Math- ematics and Computer Science, University of Leicester, Leicester, England, 1993. 8. Strictly positive definite functions on spheres, in “The International Conference on Constructive Approximation”, Tel Aviv University, Tel Aviv, Israel, 1994. 9. Distance matrices and their applications, in “The International Conference on Differential Equations”, University of Sao Paulo, Brazil, 1994. 10. Some newly developed interpolation methods, Colloquium, University of Strathclyde, Glasgow, Scotland, 1995. 11. Scattered Cardinal Hermite interpolation by positive definite functions, in “The 919th Meeting of American Mathematical Society”, Memphis, Tennessee, 1997. 12. Strictly positive definite functions on the complex Hilbert sphere, in “The Ninth International Conference on Approximation Theory”, Nashville, TN, 1998. 13. Strictly positive definite functions on spheres, in “The International Conference on Partial Differential Equations and Numerical Analysis”, Beijing, China, 1998. 14. Positive definite functions and cubature formulas on spheres, in “The Fourth International Conference on Curves and Surfaces”, Saint-Malo, France, July 1-7, 1999. 15. Positive definite functions on the circle, in “The First International Conference on Analysis and Combinatorics”, Dalian, China, 2000. 16. Strictly positive definite functions on spheres of dimension greater than one, in “The Tenth International Conference on Approximation Theory”, St. Louis, MO, 2001. 17. The structure of native spaces and their approximation property, in “The International Conference on Advances in Constructive Approximation”, Nashville, TN, 2003. 18. Approximation between native spaces, Colloquium, University of Leicester, Leicester, England, 2003. 19. Minimal Riesz energy on spheres, Colloquium, University of Missouri-St. Louis, St. Louis, MO, 2004. 20. Approximation in native spaces, in “The Tenth International Conference on Approximation Theory”, Gatlinburg, TN, 2004. 21. Minimal separation of the Riesz energy points, in “The Fourth International Workshop on Special Functions and Their Applications”, Klobster, Irsee, Germany, 2004. 22. On the separation of the minimal energy points, Seminar, Texas A&M University, College Station, TX, 2005. 23. The discrepancy and minimum separation of the minimal energy points, Colloquium, The University of Texas at Austin, Austin, TX, 2005.

4 24. Native space approximation and its applications to uniform distributions on spheres, Collo- quium, Catholic University of Lueven, Lueven, Belgium, 2005. 25. Rough native space approximation and the estimates of discrepancy on spheres, Colloquium, University of Dundee, Dundee, Scotland, 2005. 26. Direct and inverse theorems of approximation in Sobolev spaces, Seminar, City University of Hong Kong, Hong Kong, China, 2006. 27. Radial basis function approximation and applications, in “The First International Summer School on Numerical Linear Algebra”, The Chinese University of Hong Kong, Hong Kong, China, 2006. 28. Approximation of equilibrium measures via radial basis functions, Colloquium, Georgia South- ern University, March 2008. 29. Approximation of probability measures by normalized counting measures, in “Algorithms for Approximation VI”, UK, August, 2009.

30. Approximation on the Voronoi cells of the Ad lattices, Colloquium, Institute of Software, Chinese Academy of Sciences, Beijing, China, August, 2010. 31. Minimal energy configurations on spheres, Colloquium, Department of Physics, Astronomy and Materials Science, Missouri State University, 2010. 32. Approximation Theory: Reproducing Kernel View Point, a Series of Three Seminars, Institute of Mathematical Sciences, China Jiliang University, 2011. 33. Sampling scattered data with Bernstein polynomials, in “The 14th International Conference on Approximation theory, San Antonio, 2013. 34. Approximation of equilibrium measures via multiplier embedding in native spaces, Approxi- mation Day, University of Sao Paulo, ICMC, Sao Carlos, Brazil, October, 2014. 35. Theories and Applications of Conditionally Positive Definite Functions, a Short Course Con- sisting of Three Lectures in the 8th Brazilian National Conference on Analysis and Its Ap- plications, November 5 - 7, 2014, Recife, Brazil. 36. Minimal energy point sets and sphere packing, China Jiliang University, Hangzhou, China, 2015. SELECT PROFESSIONAL SERVICES 1. Organizer of the Special Session on Approximation Theory in the 873rd Regional Conference of American Mathematical Society. 2. Organizer of the Special Session dedicated to Will Light in the International Conference on Advances in Constructive Approximation. 3. Referee of the following mathematical journals: SIAM Mathematical Journal (Numerical Anal- ysis), Mathematics of Computation, Journal of Mathematical Analysis and Applications, Journal D’Analyse Mathématique, Applied and Computational Harmonic Analysis, Jour- nal of Approximation Theory, Journal of Complexity, Numerical Functional Analysis and Optimization, Journal of Neurocomputing, Applicable Analysis, Journal of Approximation Theory and Applications, Taiwanese Journal of Mathematics, Advances in Computational Mathematics, Methods and Applications of Analysis, Bulletin of Institute of Mathematics, Academia Sinica.

5 4. Organizer of the Special Session on Complexity of Algorithms in the International Conference on Algorithms on Approximation held in the Lake District of England, 2009. 5. Co-editor of the AIMS Orlando International Conference Proceedings, 2013.