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. "A block-symmetric linearization of odd-degree matrix polynomials with optimal eigenvalue condition number and backward error", by M.I. Bueno, F. Dopico, S. Furtado, L. Medina.  Calcolo (2018), 55:32.

11. "Binary Codes and Period-2 Orbits of Sequential Dynamical Systems", by C. Defant. Discrete Math. Theor. Comput. Sci. 19(2017), no.3, Paper No.10.

12. "Flexible toggles and symmetric invertible asynchronous elementary cellular automata", by C. Defant. Discrete Math., 341 (2018), 2376-2379. 

13.  "A simplified approach to Fiedler-like pencils via strong block minimal bases pencils", M. I. Bueno, F. M. Dopico, J. Perez, R. Saavedra, and B. Zykoski. Linear Algebra and its Applications,  547 (2018), 45-104.

14. "Explicit block-structures for block-symmetric Fiedler-like pencils", M. I. Bueno, M. Martin, J. Perez, A. Song, and I. Viviano.  Electronic Journal of Linear Algebra, 34 (2018), article 36.

15. "Admissibility and the C_2 Spider", A. Mejia and W. Bloomquist. Submitted.

16. "Block-symmetric linearizations of even-degree matrix polynomials with optimal eigenvalue condition number and backward error", by M. I. Bueno, J. Perez and S. Rogers, in preparation.

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