2. Fellowships and Scholarships Awards:

·                Spanish Ministry of Education Fellowship (1990-91 and 1992-93), Spain.

·                Royal Society Fellowship (1991-92), United Kingdom.

3 . Professional Services:

·               Associate Editor of East-West Journal of Mathematics.

4. Academic Experiences:

·               1991-92: Department of Mathematics, University College of North Wales, United Kingdom.

·               1993-94: Department of Mathematical Sciences, University of Wisconsin-Milwaukee, WI.

·               1994-95: Department of Mathematics, Louisiana State University at Shreveport, LA.

·               1995-96: Department of Mathematics, Indiana University, Bloomington, IN.

·               1996-97: Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM.

·               1997-99: Department of Mathematical Sciences, The University of Texas at El Paso, TX.

·               1999-Present: Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM.

5. Research Interests: research.ps

·        Infinite Dimensional Topology: The fixed point property of compact convex sets in non-locally convex linear metric spaces.

·        Fractals in Probability and Analysis: Hausdorff dimension and probability measure of fractals.

·        Numerical Analysis: Fast Fourier transforms.

 6. Publications (selected):

[1]         Probability measure functors preserving the ANR-property of metric spaces (with K. C. Ta), Proc. Amer. Math. Soc. 106(1989), 439-501.

[2]         Spaces of retractions which are homeomorphic to Hilbert space (with K. Sakai and R. Wong), Fund. Math. 136(1990), 45-52.

[3]         The group of measure preserving transformations of the unit interval is an absolute retract, Proc. Amer. Math. Soc. 110(1990), 515-522.

[4]         Decomposition of a compactum into small geometric measure sets (with S. Spiez), Topology Appl. 46(1992), 113-117.

[5]         Every needle point space contains a compact convex AR-set with no extreme points (with L. H. Tri), Proc. Amer. Math. Soc. 120(1994), 1261-1265.

[6]         The compact neighborhood extension property and local equi-connectedness (with K. Sakai), Proc. Amer. Math. Soc. 121(1994), 259-265.

[7]         No Roberts space is a counter-example to Schauder’s conjecture (with L. H. Tri), Topology, 33(1994), 371-378.

[8]         Admissibility, the locally convex approximation property and the AR-property in linear metric spaces, Proc. Amer. Math. Soc. 123(1995), 3233-3241.

[9]         Probability measure functors preserving infinite-dimensional space triples and pairs (with K. Sakai), Colloq. Math. 70(1996), 291-304.

[10]    Regular retractions onto finite dimensional convex sets and the AR-property for Roberts spaces (with N. Nhuy and T. V. An), Tsukuba J. Math., 20(1996), 281-289.

[11]    The AR-property for Roberts’ example of a compact convex set with no extreme points (with J. M. Sanjurjo and T. V. An), Proc. Amer. Math. Soc. 125(1997), Part I: 3075-3087; Part II: 3089-3098.

[12]    LC-decomposability and the AR-property in linear metric spaces (with T. V. An), Tsukuba J. Math., 21(1997), 117-128.

[13]    The finite dimensional approximation property and the AR-property in needle point spaces, J. London Math. Soc. 56(1997) 584-594.

[14]    An accurate algorithm for nonuniform fast Fourier transforms (with Q.H. Liu), IEEE Microwave and Guided Wave Letters, 8(1998), 18-20.

[15]    A rigid space homeomorphic to Hilbert space (with P. Sisson), Proc. Amer. Math. Soc. 126(1998), 85-95.

[16]    Regular Fourier matrices and nonuniform fast Fourier transforms (with Q.H. Liu), Siam J. Sci. Comp., 21(1999), 283-293.

[17]    The AR-property in linear metric spaces, (with M. Khamsi and L. Valdez-Sanchez), Topology Appl. 109(2001), 267-284.

[18]    Lambda-hyperconvexity in metric spaces (with M. A. Khamsi, H. Knaust and M. O’Neill), Nonlinear Analysis - Theory, Method & Applications, 43(2001), 21-31.

[19]    Iterated function systems of finite type and the weak separation property, Proc. Amer. Math. Soc., 130(2002), 483-487. 19paper.ps

[20]    Rigid spaces and the AR-property, (with J. Jaworowski, N. Nhuy, and P. Sisson), Tsukuba J. Math., to appear. 20paper.ps

[21]    The local dimension of fractal measures associated with uniformly distributed probabilistic systems (with T.Y. Hu), Trans. Amer. Math. Soc., submitted. 21paper.ps

[22]    The local dimension of fractal measures associated with the (0; 1; 3)-Problem (with T.Y. Hu and T. Wang), Proc. Amer. Math. Soc., submitted. 22paper.ps

[23]    The Heighway dragon revisited (with S.M. Ngai), Trans. Amer. Math. Soc., submitted. 23paper.ps