# Recent papers by Ron Umble

A Topologically Induced 2/in-2/out Operation on Loop Cohomology,” J. Math. Sci. 3 (2012) 30-37, offprint

Tensor Products of A_\infty Algebras with
Homotopy Inner Products (with T. Tradler), preprint

Morphisms of A_\infty-Bialgebras and Applications (with S. Saneblidze), preprint

On the Z_2-Cohomology of 3D Polyhedral Approximations (with R. Gonzales-Diaz and J. Lamar), preprint

Edge Tessellations and Stamp Folding Puzzles (with M. Kirby), Mathematics Magazine, 84 (2011) 283–289.

A_\infty-Bialgebras of Type (m,n) (with A. Berciano and S. Evans), preprint

Gereralizations of the Brachistochrone Problem (with J. Gemmer and M. Nolan), Pi Mu Epsilon Journal, 13(4) (2011), 207-218

Higher Homotopy Hopf Algebras Found: A Ten Year Retrospective, "Higher Structures in Geometry and Physics in honor of M. Gerstenhaber and J. Stasheff," Cattaneo, Giaquinto and Xu Eds.,Progress in Math. 287, Birkhauser, New York, 2011, 343-362

Some Naturally Occurring Examples of A_\infty-Bialgebras (with A. Berciano), J. Pure and Appl. Alg., 215 (2011), 1284–1291

Matrads, Biassociahedra, and A_\infty-Bialgebas (with S. Saneblidze), J. Homology, Homotopy and Appl., 13(1) (2011), 1–57

Open Questions Related to A_\infty Structures in a Computational Framework, in: Conrtibuciones Cientificas en Honor De Mirian Andres Gomez (L. Lambia, A. Romero, J. Rubio, Eds.), Servicio de Publicaciones, Universidad de La Rioja, Logrono, Spain (2010) 171-176

Periodic Orbits for Billiards on an Equilateral Triangle (with A. Baxter), American Mathematical Monthly, 115(8) (2008), 479-491

Minimal Paths on Some Simple Surfaces with Singularities (with J. Mohler), Pi Mu Epsilon J., 12(8) (2008), 461-472

Structure Relations in Special A_\infty-Bialgebras, J. Math Sci., 152(3) (2008), 443-450. Translated from: Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and its Applications), 43, Topology and Its Applications, (2006) 136-143.

The Biderivative and A_\infty-Bialgebras (with S. Saneblidze), J. Homology, Homotopy and Appl., 7(2) 2005), 161-177

Diagonals on the Permutahedra, Multiplihedra and Associahedra (with S. Saneblidze), J. Homology, Homotopy and Appl., 6(1) (2004), 363-411

A Diagonal on the Associahedra (with S. Saneblidze), preprint

Obstructions to Deformations of DG Modules (with T. Armstrong), Proc. AMS, 129(12) (2001), 3447-3452

The Deformation Complex for DG Hopf Algebras, J. Pure and Appl. Alg., 106 (1996), 199-222