MATH Summer Research Program

University of California, Santa Barbara

Here we present some of the papers that the participants in our program have written, submitted, and/or published recently:

1. "Distribution of the exponents of primitive circulant matrices in the first four boxes of  Zn", by M.I. Bueno, K. Fang, S. Fuller, and S. Furtado. Involve  5(2012), 187-205.

2. "The solution of the equation AX+X*B=O", by F. De Teran, F. M. Dopico, N. Guillery, D. Montealegre, and N. Reyes. Linear Algebra and its Applications 438(2013), 2817-2860.

3. "The Alexander and Jones Polynomials through representations of rook algebras", by S. Bigelow, E. Ramos, and R. Yi.  Journal of Knot Theory and its Ramifications, 21(2012), 18 pp.

4. "Systematic Stochastic Reduction of Inertial Fluid-Structure Interactions subject to Thermal Fluctuations", by P. Atzberger and G. Tabak. SIAM J. Appl. Math., 75(4),  (2015), 1884-1914.

5. "Presentation of the Motzkin Monoid", by K. Hatch, M. Ly, and E. Posner. Technical report.

6. "A parametric model for determining consensus priority vectors from fuzzy comparison matrices", by S. Chouinard, E. Dopazo, J. Guisse, and K. Lui. Fuzzy Sets and Systems, vol. 246 (2014), 49-61.

7. "The kernel of the matrix ij (mod n) when n is prime", by M.I. Bueno, S. Furtado,  J. Karkoska, K. Mayfield, R. Samalis, and A. Telatovich.  Involve, 9-2 (2016), 265-280.

8. " A Decomposition of Parking Functions By Undesired Spaces ," M. Bruce, M. Dougherty, M. Hlavacek, R. Kudo, and I. Nicolas. Electr. Journal of Combinatorics,  23 (3) (2016), p3.32.

9. "On the sign characteristic of Hermitian linearizations in DL(P)", by J. Breen, M.I. Bueno, S.  Ford, and S. Furtado.   Linear Algebra and its Applications, 519 (2017), 73-101.

10. "Conditioning and backward error of block-symmetric block-tridiagonal linearizations of matrix polynomials", by M.I. Bueno, F. Dopico, S. Furtado, L. Medina. Submitted.

11. "Binary Codes and Period-2 Orbits of Sequential Dynamical Systems", by C. Defant. Preprint.

12. "Enumerating Periodic Points of Certain Sequential Dynamical Systems", by C. Defant. Preprint. 

13.  "A unified approach to Fiedler-like pencils via strong block minimal bases pencils", M. I. Bueno, F. M. Dopico, J. Perez, R. Saavedra, and B. Zykoski. Submitted.

14. "Block-structures for block-symmetric Fiedler-like pencils", M. I. Bueno, M. Martin, J. Perez, A. Song, and I. Viviano. In preparation.

The UCSB Mathematics Summer Research Program for Undergraduates  is supported by the National Science Foundation.