Unpublished
Dmitry Berdinsky, Prohrak Kruengthomya, "Finite Automata Encoding Piecewise Polynomials" // [arXiv]
Published
Kruengthomya P., Berdinsky D., "Extending the Synchronous Fellow Traveler Property", Asian-European Journal of Mathematics, V. 17, N. 10, 2450069, pp. 1-23 (2024) // [publisher] [arXiv]
Kruengthomya P., Berdinsky D., "Cayley Linear–Time Computable Groups", journal of Groups, Complexity, Cryptology, V. 15, N. 2, pp. 1–22 (2024) // [publisher] [arXiv]
Berdinsky D., Jain S., Khoussainov B., Stephan F., "String Compression in FA–Presentable Structures", Theoretical Computer Science, 947, 113705, pp. 1-10 (2023) // [publisher] [arXiv]
Berdinsky D., Elder M., Kruengthomya P., "Cayley Polynomial-Time Computable Groups", Information and Computation, 288, 104768, pp. 1-15 (2022) // [publisher] [arXiv]
Berdinsky D., Elder M., Taback J., "On the geometry of Cayley automatic groups", International Journal of Algebra and Computation, V. 32, N. 03, pp. 383-409 (2022) // [publisher] [arXiv]
Berdinsky D., Elder M., Taback J., "Being Cayley automatic is closed under taking wreath product with virtually cyclic groups", Bulletin of the Australian Mathematical Society, 104, pp. 464–474 (2021) // [publisher] [arXiv]
Berdinsky D., Kruengthomya P., "Nonstandard Cayley Automatic Representations for Fundamental Groups of Torus Bundles over the Circle", Lecture Notes in Computer Science, Springer, Cham, V. 12038, pp. 115-127 (2020) // [publisher] [arXiv]
Berdinsky D., Trakuldit P., "Towards quantitative classification of Cayley automatic groups", East-West Journal of Mathematics, V. 20, N. 2, pp. 107-124 (2018) // [publisher] [arXiv]
Berdinsky D., Trakuldit P., "Measuring Closeness Between Cayley Automatic Groups and Automatic Groups" In: Klein S., Martín-Vide C., Shapira D. (Eds.): Language and Automata Theory and Applications 2018. Lecture Notes in Computer Science, Springer, Cham, V. 10792, pp. 245-257 (2018) // [publisher] [arXiv]
Berdinsky D., Vyatkin Y., "Willmore-like functionals for surfaces in 3-dimensional Thurston geometries", Osaka Journal of Mathematics, V. 54, N. 1, pp. 75-83 (2017) // [publisher] [arXiv]
Berdinsky D., "Cayley automatic groups and numerical characteristics of Turing transducers", S. Brlek and C. Reutenauer (Eds.): Developments in Language Theory 2016, Lecture Notes in Computer Science, V. 9840, pp. 26-37 (2016) // [publisher] [arXiv]
Berdinsky D., Khoussainov B., "Cayley automatic representations of wreath products", International Journal of Foundations of Computer Science, V. 27, N. 2, pp. 147-159 (2016) // [publisher] [arXiv]
Berdinsky D., Kim T., Cho D., Bracco C., Kiatpanichgij S., "Bases of T-meshes and the refinement of hierarchical B-splines", Computer Methods in Applied Mechanics and Engineering, V. 283, pp. 841-855 (2015) // [publisher] [arXiv]
Berdinsky D., Khoussainov B., "On automatic transitive graphs", A.M. Shur and M.V. Volkov (Eds.): Developments in Language Theory 2014, Lecture Notes in Computer Science, V. 8633, pp. 1-12 (2014) // [publisher] [HAL]
Bracco C., Berdinsky D., Cho D., Oh M., Kim T., "Trigonometric Generalized T-splines", Computer Methods in Applied Mechanics and Engineering, V. 268, pp. 540–556 (2014) // [publisher]
Berdinsky D., Kim T., Bracco C., Cho D., Mourrain B., Oh M., Kiatpanichgij S., "Dimensions and bases of hierarchical tensor-product splines", Journal of Computational and Applied Mathematics, V. 257, pp. 86–104 (2014) // [publisher] [HAL]
Berdinsky D., Kim T., Bracco C., Cho D., Oh. M, Seo Y., Kiatpanichgij S., "Iterative refinement of hierarchical T-meshes for bases of spline spaces with highest order smoothness", Computer-Aided Design, V. 47, pp. 96-107 (2014) // [publisher] [HAL]
Berdinsky D., Oh M., Kim T., Mourrain B., "On the problem of instability in the dimension of a spline space over a T-mesh", Computers & Graphics, V. 36, N. 5, pp. 507–513 (2012) // [publisher] [HAL]
Berdinsky D., "On constant mean curvature surfaces in the Heisenberg group", Siberian Advances in Mathematics, V. 22, N. 2, pp. 75-79 (2012) // [publisher] [arXiv] [pdf]
Berdinsky D., "On minimal surfaces in the Heisenberg group", A collection of papers of the International Conference "Geometry and Analysis", Kemerovo, Russia, 2011, Bulletin of Kemerovo State University, V. 3/1, N. 47, pp. 34–38 (2011) // [publisher]
Berdinsky D., Rybnikov I., "On orthogonal curvilinear coordinate systems in constant curvature spaces", Siberian Math. Journal, V. 52, pp. 394-401 (2011) // [publisher] [arXiv] [pdf]
Berdinsky D., "On some generalization of the Willmore functional for surfaces in SL2", Siberian Electronic Mathematical Reports, V. 7, pp. 140-149 (2010) // [publisher] [HAL] [pdf]
Berdinsky D., Taimanov I., "Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional", Siberian Math. Journal, V. 48, N. 3, pp. 395-407 (2007) // [publisher] [arXiv] [pdf]
Berdinsky D., Taimanov I., "Surfaces in three-dimensional Lie groups", Siberian Math. Journal, V. 46, N. 6, pp. 1005-1019 (2005) // [publisher] [arXiv] [pdf]
Reports
Berdinsky D. and Taimanov I., Oberwolfach Reports, V. 4, N. 2, pp. 1353–1358 (2007) // [publisher]
Theses
Berdinsky D., "Representations of transitive graphs by automata", PhD Thesis (Computer Science), The University of Auckland (2017) // [publisher] [pdf]
Berdinsky D., "The Weierstrass representation of surfaces in three-dimensional Lie groups and its applications", PhD Thesis (Mathematics), Sobolev Institute of Mathematics (2009) // [synopsis] [pdf]