Texts

My texts

Here I keep anything I have written and put out to public access.

Notes

Logic

  1. Vladislav Shubin. “Formal Philosophy: Notes”. (in Russian) link: Владислав Шубин. «Формальная философия: конспект»

  2. Vladislav Shubin. “Notes in Type theory”. (in Russian) link: Владислав Шубин. «Теория типов: конспект»

Thesis

Master Thesis: “Berry Phase for Quantum Graphs”

Text is available here .

  • Supervisor: Pavel Kurasov

Contributions:

  • Studied topology change via parameter-dependent vertex conditions.
  • Derived explicit continuous eigenfunction families.
  • Showed that topology change induces a nontrivial Berry phase $pi$ for real-valued eigenfunctions.
  • Established a connection between topology change and the structure of operator domains.

Bachelor Thesis: “Bernstein Polynomials and MacWilliams Transform”

Text is available here (in Russian.)

  • Supervisor: Nikita Gogin, Vladimir Kuznetsov

Contributions:

  • Studied MacWilliams (Krawtchouk) transform and its applications in approximation theory.
  • Found new formulae for Bernstein and Chebyshev polynomials.
  • Developed an algorithm for computing Bernstein polynomials.

Preprints

  1. Pavel Kurasov, Vladislav Shubin, Axel Tibbling. “Berry’s phase under topology change”. doi: https://doi.org/10.48550/arXiv.2605.10798

Conference Proceedings

  1. Vladislav Shubin. “Investigation of ϕ-radical numbers”. In: 73rd Scientific Conference of Sudents and Young Scientist. Petrozavodsk, Russia, 2021.

  2. Vladislav Shubin and Nikita Gogin. “Bernstein Polynomials and MacWilliams transform”. In: International Conference Polynomial Computer Algebra ’2023’ (PCA’2023). Saint-Petersburg, Russia, 2023.

  3. Vladislav Shubin and Nikita Gogin. “Binomial Coefficients as Functions of their Denominator; Another Primality Criteria for Natural Integers”. In: International Conference Polynomial Computer Algebra ’2024’ (PCA’2024). Saint-Petersburg, Russia, 2024.

  4. Vladislav Shubin and Nikita Gogin. “Prime Power Conjecture for Projective Planes”. In: International Conference Polynomial Computer Algebra ’2025’ (PCA’2025). Saint-Petersburg, Russia, 2025.

  5. Vladislav Shubin and Ivan Ushakov. “MacWilliams Transform with Binomial Weights”. Polynomial Computer Algebra, 2026.

OEIS contributions

I authored the following OEIS sequences: A355045, A355059, A337775, A337776.

and also contributed to: A000108