Research Activity

SCHOLARLY PUBLICATIONS:

 

“Symmetries of fractal tilings” with Maria Salcedo, Fractals, to appear.


“Nanoassembly of a Fractal Polymer: A Molecular ‘Sierpinski Hexagonal Gasket’” with George R. Newkome, Pingshan Wang, Charles N. Moorefield, Tae Joon Cho, Prabhu P. Mohapatra, Sinan Li, Seok-Ho Hwang, Olena Lukoyanova, Luis Echegoyen, Violeta Iancu, and Saw-Wai Hla, Science 312 (23 June 2006), 1782-1785.

 


"Outer boundaries of self-simlar tiles," with S.Drenning, T. Price and R. Strichartz, Experimental Mathematics, Vol. 14 (2005), No. 2, 199-209.

"Analysis of an irregular Sierpinski triangle," with Matthew C. Palmer, Fractals Vol. 8, No. 1 (2004).

"Determining the area of fractal tilings," with Miyuki Breen, Pi Mu Epsilon Journal, Spring 2003.

"Complex bases and fractal tilings" with Sara Hagey, Mathematical Gazette 85 no. 503 (2001), 194–201.

"Analyzing the Value of a Transitional Mathematics Course" with William A. Blue, in B. Gold, S. Keith, W. Marion, eds., Assessment Practices in Undergraduate Mathematics, MAA Notes # 49, Mathematical Association of America, Washington DC, 1999, pp. 64-67.

"Fractal Tilings in the Plane" Mathematics Magazine, with R.B. Darst and T. E. Price, Vol. 71, No. 1, February, 1998, 12-23.

"Some remarks on the evaluation of ", with T.E. Price, Mathematics Magazine,Vol. 70, No. 1, February 1997, 63-67.

A Transition to Advanced Mathematics by D. Smith, M. Eggen and R. St. Andre. Foundations for Advanced Mathematics by C. Avelsgard. Introduction to Advanced Mathematics by W. Barnier and N. Feldman. An extended review, American Mathematical Monthly, February, 1991.

"Properties of projections obtained by averaging certain polynomial interpolants," with T.E. Price, Approximation Theory, Tampa (Lecture Notes in Mathematics 1287 E.B Saff, Ed.) Springer-Verlag 1987, 132-145.

"Near-best approximation by averaging polynomial interpolants," with T.E Price, IMA Journal of Numerical Analysis 7(1987), 107-122.

"An extension theorem for disjointly additive functionals on Lp," with R.B Darst, Houston Journal of Mathematics 9(1983), 383-386.

"A representation for additive functionals on Lp-spaces," Pacific Journal of Mathematics, 66(1976), 221-234.


FELLOWSHIPS AND GRANTS:

 

NSF-REU: Research Experiences for Undergraduates: Algebra, Number Theory and Applications, 2005-2007.

Summer Research Grant - University of Akron, Summer 2001.

MAA/Tensor Grant, June 1998-June 2000.

Summer Research Grant - University of Akron, Summer 1997.

Faculty Research Grant, University of Akron, March 1993-January 1994.

Ohio Board of Regents Grant, March 1993-January 1994.

Educational Research and Development Grant, University of Akron, June 1992-June 1993.

Research Challenge Enhancement Grant, Ohio Board of Regents, June 1990-June 1991.

Summer Research Grant - University of Akron, Summer 1989.


RESEARCH PROJECTS WITH STUDENTS

"Random Sierpinski triangles and fractal interpolation" with Samantha Fales.

"Complex bases and fractal tilings", with Sara Leugers.

"Fractal tilings derived from non-integer bases" with Rebecca Brown.

"Analysis of an irregular Sierpinski triangle" with Matthew Palmer.

"Determining the area of fractal tilings" with Miyuki Breen.

"Cystallographic fractal tilings" with Maria Salcedo.

"Iterating Penrose tilings" with Naomi Cummings.

“Self-similar tilings of nilpotent Lie groups” with R. Black, P. Hudelson, L. Lackney and J. Rohal.

“Self-intersection properties of generalized Koch curves” with M. Cantrell and R. Price.


INVITED PROFESSIONAL PRESENTATIONS

 

“Curious curves,” Ohio MAA, April 2007

 

“Fractal tilings of the plane,” Carnegie Mellon University, February 2007.

 

“Preparing for a professional leave” Ohio NExT, March 2006.

"Fractal tilings," colloquium, Grove City  College, October 2003.

"Fractal geometry and its applications," induction ceremony, Malone College, April 2004.

"Random Sierpinski triangles," Retiring President's Address, Ohio MAA, March 2001.

"Fractal tilings in the plane", Indiana-Purdue University, Fort Wayne, December 1999.

"Fractal geometry", Arts and Science Honors Colloquium, November,1997 and February, 1995.

"Fractal tilings in the plane", Westminster College colloquium series, November, 1994.

"Women in mathematics: balancing the equation", Gender Equity in Secondary Education, Brunswick High School, October, 1994.

"Integer matrices and fractal tilings of the plane", Colorado State University colloquium, March, 1994.

"Women in Mathematics", Women in Science and Engineering Workshop, The Ohio Academy of Sciences and The University of Akron, November, 1989.

"Cantor Sets and Cantor Functions." Westminster College colloquium series, New Wilmington, Pa., February, 1989.

"Near-best approximation by averaging polynomial interpolants." Constructive Function Theory Conference Edmonton Alberta, July, 1986.

"Computer science in the high school." Akron Public Schools Teacher In-service Day, October,1983.

"Women and Mathematics." Math Anxiety Workshop, The University of Akron, July, 1982 and July, 1983.

"Additive Functionals on Lp, 0 < p < 1." Colloquium at University of Guelph, Ontario, February, 1981.

"Math Anxieties." Sex Roles and Identities Seminar, The University of Akron, July, 1979 and March, 1980.

"Women and Mathematics." Akron Public Schools Teacher In-service Day, August, 1979.
 


PROFESSIONAL PRESENTATIONS:

"Boundaries of fractal tiles," Ohio MAA, Columbus, March 2003.

"Complex bases and fractal tilings", Ohio MAA, Columbus, October, 1998.

"Random Sierpinski triangles and fractal interpolation", AMS/MAA Meeting, Baltimore, January, 1998.

"The Hausdorff measure of certain subsets of the Cantor set.", AMS/MAA Meeting, San Francisco, January,1995.

"Fractal Tilings in the plane", Pi Mu Epsilon Conference, Miami University, Oxford, OH, October, 1994.

"Analyzing the value of a transitional mathematics course in the undergraduate mathematics program" AMS/MAA Meeting, MAA session on Assessment Programs for the Undergraduate Major, January, 1993, San Antonio.

"Extensions of a theorem of Walsh." Texas International Symposium on Approximation Theory, January, 1992, Austin, TX.

"A look at bridging the gap." MAA Ohio Section Meeting, October, 1990, Marietta, Ohio.

"Polynomial interpolants and least squares approximation." MAA Ohio Section Meeting, October, 1986, Toledo, Ohio.

"Near-best approximation by averaging polynomial interpolants," MAA Ohio Section Meeting, April 1983, Marietta Ohio.

"Averaging interpolating polynomials." AMS/MAA Meeting January 1983, Denver.

"An extension theorem for additive functionals on Lp." AMS/MAA Meeting, January, 1981, San Francisco.

"Continuous linear functionals on Lp-spaces." AMS/MAAMeeting, January, 1977, St. Louis.

"Some Cantor sets and Cantor functions." MAA Seaway Section Meeting, November, 1976, Binghamton, New York.

"Linear and nonlinear functionals on the spaces Lp." AMS/MAA Meeting, January, 1975, Washington, D.C.