Semjon Adlaj

Scientific Researcher

Section of Stability Theory and Mechanics of Controlled Systems

Division of Complex Physical and Technical Systems Modeling

A.A. Dorodnicyn Computing Centre of the Russian Academy of Sciences

**e-mail**: SemjonAdlaj@gmail.com

Several Fundamental Publications

- On Rubik's Cube (written in Russian and retrieved from the past millenium).
- Classification and investigation of stability of thread equilibria in a linear parallel force field. A monograph, written in Russian in 2011 and published in 2018.
- An analytic unifying formula of oscillatory and rotary motion of a simple pendulum (dedicated to the 70
^{th}birthday of Jan Jerzy Slawianowski, written in 2013 and updated in 2014). Proceedings of International Conference “Geometry, Integrability, Mechanics and Quantization”, Varna, Bulgaria, 2014, June 6-11. Printed by “Avangard Prima”, Sofia, Bulgaria, 2015: 160-171. - Multiplication and division on elliptic curves, torsion points and roots of modular equations. Zapiski Nauchnykh Seminarov POMI (485), 2019: 24-57. An article written in 2014 (with references updated in 2019). An highly amusing blog cites it here 5次方程式の解の公式を求める. It was also cited in an article by Stefan Schmid.
- An arithmetic-geometric mean of a third kind! (a paper, written in 2015, with references updated in 2019, containing “perfect” formulae for calculating three kinds of complete Elliptic Integrals). Lecture Notes in Computer Science, volume 11661: 37-56. Presented on August 30, 2019 at the 21
^{st}International Workshop on Computer Algebra in Scientific Computing, yet it was earlier cited in an article by Hea Kejing, Zhoua Xiaoqiang and Lin Qian. See also their footnote at the bottom of page 123. - Torque free motion of a rigid body: from Feynman wobbling plate to Dzhanibekov flipping wingnut. A 15-page paper, written in 2017 (with references updated in 2019), where a symmetric (in the moments of inertia) expression for the rate of precession is obtained, as well as, the relevance of constructing the Galois critical axis, for describing the motion of both “Burke's twisting tennis racket” and “Dzhanibekov's flipping wingnut”, is shown.

Selected Seminar Talks and a Lecture

- Torsion points on elliptic curves and modular polynomial symmetries, presented on September 24, 2014 at the joint MSU-CCRAS Computer Algebra Seminar. Two relevant short papers by Helmut Ruhland are The inverse of the modular invariant and Constructing equalities.
- Two talks on “Dzhanibekov screw” (in Russian) were delivered on October 26, 2016 and May 16, 2018 at the Egorov seminar on the mechanics of space flight, conducted at the Moscow State University (MSU) by Victor Sazonov.
- Modular equations and fundamental problems of classical mechanics, presented on January 31, 2019 and met with organized resistance, where deficient qualifications of A.S. Sumbatov, S.V. Pikulin, A.A. Burov and S.Ya. Stepanov were vividly exposed as V.I. Vlasov rushed to prematurely terminate his ill-organized seminar, which (nevertheless, that is, no thanks to him) turned out being a success. The talk, along with the subsequent discussion, was eventually translated to English (with Francois Lamarche and Simon Kreymerman as translation editors). My talk subsequently propmted a “new task for senior students by Victor Sazonov” (which I received on April 7, 2019) for discussion at a methodical seminar of the Department of Theoretical Mechanics and Mechatronics of MSU. That “new task” required my clarifying response (which I sent on April 26, 2019).
- Complex periods, time reversibility and duality in classical mechanics, coauthored with Francois Lamarche (Teledyne LeCroy, USA) and presented on November 26, 2019 at the Russian Interdisciplinary Temporology Seminar in MSU. My talk prompted a sharp, yet expediently settled, discussion with Oleg Zubelevich.
- On forming basic integration skills for freshmen, presented on May 12, 2021 at the Scientific and Methodical Seminar of the Department of Mathematics in the National University of Science and Technology MISiS.
- Two talks were delivered on September 1, 2022 and March 2, 2023 at the Seminar on the History of Mathematics of the Saint Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences. The set of slides of the first talk “on the second memoir of the last letter of Évariste Galois” is a subset of the slides of the second talk on “Modular equations and Galois elliptic function”.
- A lecture on Borwein integrals read on April 17, 2023, within a course on the theory of functions of a complex variable, for sophomores at Gubkin State University.

Selected Workshops and Conferences

- Iterative algorithm for computing an elliptic integral, presented on 2011.06.03.
- Highly efficient arithmetic of elliptic curves, presented on 2012.05.23.
- Elliptic and coelliptic polynomials, presented on 2014.05.21.
- Spin to wobble calculation and symbolic integration, presented on 2016.05.24.
- Galois primes and modular equations, presented on 2018.05.21.
- Symbolic integration of elliptic functions, presented on 2019.05.23.
- An explicit procedure for calculating the perimeter of an ellipse, presented on 2021.05.24.
- Tether equilibria in proximity to a circularly orbiting satellite and their stability criteria, presented on 2011.10.19.
- Mechanical interpretation of negative and imaginary tension of a tether in a linear parallel force field, presented on 2012.02.02.
- Isoperimetric problem singularities, presented on 2012.07.03.
- Applying singularity theory to investigating stability of isoperimetric problem solutions, presented on 2014.07.08.
- Galois modularity as foundation of highly efficient exact algorithms in classical mechanics, presented on 2018.07.09.
- Back to the pendulum for an exact explicit solution! Presented on 2015.07.03.
- Dzhanibekov's flipping wingnut and Burke's twisting tennis racket, presented on 2017.07.07.
- Modular polynomial symmetries, presented on 2014.04.16.

- New unexpected solutions to well-known differential equations, presented on 2015.04.15.

- Dzhanibekov’s flipping nut and Feynman’s wobbling plate, presented on 2016.04.20.

- Two formulas of planetary motion, presented on 2017.04.19.

- Back to solving the quintic, depression and Galois primes, presented on 2018.04.20.
- Galois elliptic function and its symmetries, presented on 2019.04.18.
- Rigid body motion symmetries, presented on 2020.10.15.
- Orienting pseudovectors and polhodes, presented on 2021.04.19.
- The generalized arithmetic-geometric mean, presented on 2022.05.02.
- Algebraic methods in Theoretical Mechanics was scheduled to be presented on 2023.04.20. The title of the talk was chosen to coincide with an announcement of a seminar.
- The Euler top and the Lagrange top as two special cases of the Galois top, presented on 2024.04.17.
- Эффект Джанибекова, presented on 2017.10.25.
- Mirror symmetry in classical mechanics, presented on 2019.12.11.
- Rigid body motion orientation, presented on 2021.12.08.
- On a little-known dinkum revolutionary contribution of Évariste Galois, presented on 2018.05.31.
- Elliptic Integrals, Functions, Curves and Polynomials, presented on 2019.07.23.
- On the auxiliary role of computer tools in the clarification and proliferation of fundamental geometric constructions, presented on 2021.07.29.
- The thrive for simplicity in Science Teaching, presented on 2023.07.25.

7

XV

(dedicated to the centennial birthday of Nikolai Mikhailovich Korobov)

Worldwide Collaboration

- 中國科學院 The Chinese Academy of Sciences had published in its journal 主题 (Mathematical Advance in Translation) the article 关于椭圆周长的一个完美的计算公式 which is a translation (姚景齐 译 赵春来 校) of my article An eloquent formula for the perimeter of an ellipse, as published in the Notices of the AMS,
**59**(8): 1094-1099. The naming “Gauss-Euler algorithm”, suggested in the article, was (immodestly) criticized by Richard Brent in “a letter to the editor”. His letter (no less evidently unfairly) avoids naming the discoverer of fast multiplication: Anatoly Karatsuba. An implementation of MAGM for calculating the magnetic field near a loop of current was carried out by Francois Lamarche. That concept originated in calculating the length of a thread in a linear parallel repelling force field, as told in my 2018 monograph Равновесие нити в линейном параллельном поле сил. A few programs in RPN/FOCAL (HP41) for ellipse perimeter calculation are provided by Pascal Dagornet. - A Mathematical Modeling Team at the Department of Theoretical Mechanics of the Ural Federal University (headed by Natalia E. Misura & Euigene A. Mityushov) was the first to present (in 2018) an animation of the critical torque free motion of a rigid motion, which ought not be confused with any other (non-critical) motion in its “vicinity”. Such critical motion is fully clarified in a joint paper of four authors, where an axis (rightfully named the Galois axis) is shown to rotate uniformly whether or not a “reversal” (in two distinct “mirror-symmetric” ways!) of the intermediate axis of inertia occurs. The joint paper was preceded by a short talk on November 09, 2017 (in Russian), and succeeded by a presentation, where the
Galois axis was brought to a shining light, on Januarya 29, 2019. The Galois axis made its debut to a textbook in Кватернионные модели в кинематике и динамике твердого тела, 2020: 88. - 有限会社 大平技研 Ohira Tech is the first company in the world to implement (a pilot version of) the rotating celestial sphere. The invention is coauthored with the president of the company Takayuki Ohira 貴之 大平. A priority invention date of July 1, 2019 is assigned by patent № 2730227.

Few Short Papers

- Duality of solutions of thread equilibrium problem in attracting and repelling fields of parallel forces (in Russian). Issues on Motion Stability and Stabilization. Moscow, CCRAS 2009: 110-118.
- Iterative algorithm for computing an elliptic integral (in Russian). Issues on Motion Stability and Stabilization. Moscow, CCRAS 2011: 104-110.
- Eighth lattice points. Written on May 30, 2011 to be temporarily posted at “arXiv” (till May 10, 2024).
- An action of the Klein 4-group on the angular velocity. Zapiski Nauchnykh Seminarov POMI (528), 2023: 47-53.

Few Excerpts and Highlights

- The arc length of the sine curve.
- A heptagon constructed!
- A point of order 8.
- Four special values of the Modular Invariant.
- Triple-pair invariance theorem (in Russian).
- Duality of base-coordinate transformation.
- Duality of equilibria of a Simple Pendulum.
- The Galois top invariant of motion.

Few interdisciplinary (non-technical) concepts, explained to curious practitioners

- Performance of Binary Tests. A 4-page article, explaining the dual-concepts of sensitivity and specificity.
- The Monty Hall problem settled. Examples of hidden assumptions behind short answers to ill-posed questions.

Educational Issues and Concerns

- Mathematics as universal language in school education (in Russian).
- A trapezium which fails to exist (in Russian).
- A typical exam problem, much telling of the examiners (in Russian).

a Tribute to Music

- Robert Schumann “Fantasy Dance”, performed on March 15, 2018.
- First Composition for Cello and Piano, performed on May 24, 2018.
- First Piano Exam, excellently passed on April 26, 2019.
- A Little Concert, performed on May 8, 2020, in dedication to the 75
^{th}anniversary of the unconditional capitulation of fascist germany. - Jean Sibelius etude in A minor, performed on February 18, 2021.

an Invitation

“Математика - язык естествознания” is an open club for all interested schoolers,

along with their companions (whether family members or teachers).

Wide range of topics are exposed by active scientists and discussed at many levels

(while excluding “teaching and preaching” methodology),

eventually involving all (necessarily including the youngest) participants.

The club organizes an annual conference for aspired school age researchers.