When we know how the physical world works, we will find out what we are needed for in this world.

Studied at Moscow Aviation Instrument Making College named after S. Ordzhonikidze, qualification - “Technician-mechanic, aviation devices”.

Served in the Soviet army, qualification - “Technician-heating”.

Studied at Peoples’ Friendship University named after P. Lumumba (now RUDN University), qualification - “Physicist”.

Postgraduate course of Peoples’ Friendship University named after P. Lumumba (now RUDN University) (Theoretical Physics), thesis on “Research of gravitational fields and cosmological models in torsion spaces” for the degree of Candidate of Physical and Mathematical Sciences was defended.

Senior lecturer at the Faculty of Physics, Mathematics and Natural Sciences of Peoples’ Friendship University named after P. Lumumba (now RUDN University), worked in the Department for work with students.

Research internship at the University of Houston, Houston, USA.

Senior lecturer, associate professor of the Department of Natural Sciences of the Preparatory Faculty of Peoples’ Friendship University named after P. Lumumba (now RUDN University).

Head of the Department of Physics: **1992-2000** - of the Preparatory Faculty, **2000-2020** – of the faculty of Russian Language and General Educational Disciplines, **since 2020** - of Educational and Scientific Institute of Gravitation and Cosmology RUDN University.

Vice-Rector for Academic Affairs of RUDN University.

First Vice-Rector - Vice-Rector for Academic Affairs of RUDN University.

Director of Educational and Scientific Institute of Gravitation and Cosmology RUDN University.

Order of Friendship of Peoples for fruitful activities in the development of science, education, health and culture was awarded.

Member of the Commission of the Ministry of Education and Science on the implementation of the Bologna Agreement in the Russian Federation.

Thesis on “Research of quaternion spaces and their relationship with reference systems and physical fields” for the degree of Doctor of Physical and Mathematical Sciences was defended.

Member of the Council for Quality of Education of the Federal Service for Supervision of Education and Science.

Title of honorary worker of higher education of the Russian Federation for services to scientific and pedagogical work and training of highly qualified specialists was awarded.

Gratitude of the President of the Russian Federation for fruitful long-term work in the higher education system.

### Teaching

- The developer of the course: Quaternion algebra, fractal space, and General theory of mechanics iversity.org of Springer Nature.

https://iversity.org/en/courses/quaternion-algebra-fractal-space-and-general-theory-of-mechanics - The main idea of the course is to learn that a number of physical laws, initially discovered in an experiment and described by mathematical formulas, exist in the mathematical environment of hypercomplex numbers.

**The author of monographs:**

- Yefremov A.P. The fractal structure of space entails origin of Pauli equation / Gravitation Cosmology, 2019, 25(4), pp. 305-309.

This study links the fractal structure of physical space-time to quantum-mechanical laws. It is shown that primitive distortions of the pregeometric surface, a fractal cell of 3D space, gives birth to a condition eliminating the metric defect while providing “eternal validity” of the exclusive algebras (of real, complex, and quaternion numbers). Written in the physical units typical for the micro-world entities, this condition acquires the precise form of the Pauli equation describing mechanics of the quantum electron with spin.

https://www.researchgate.net/publication/337838143_The_Fractal_Structure_of_Space_Entails_Origin_of_Pauli's_Equation - Yefremov A.P. General theory of particle mechanics arising from fractal space / Gravitation and Cosmology, 2015, 21(1), pp. 19-27.

We trace the logical line of formulating a theory of mechanics founded on the basic relations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical and relativistic mechanics can be regarded as mathematical consequences of a single condition of stability of exceptional algebras of real, complex and quaternion numbers under transformations of primitive constituents of their units and elements. In the course of the study, the notion of a basic fractal surface underlying the physical three-dimensional space is introduced, and an original geometric treatment (admitting visualization) of some formerly considered abstract functions (mechanical action, space-time interval) are suggested.

https://www.researchgate.net/publication/276695536_General_Theory_of_Particle_Mechanics_arising_from_a_fractal_surface - Yefremov A. P. General theory of mechanics of particles, arising from the fractal space

It is shown that the physical equations of quantum, classical, and relativistic mechanics can be considered as mathematical consequences of a single condition for the stability of exceptional algebras of real, complex, and quaternion numbers under transformations of their primitive constituent units and elements. The research introduces the concept of a basic fractal surface that underlies the physical three-dimensional space, and offers an original geometric interpretation (allowing visualization) of some previously considered abstract functions (mechanical action, space-time interval).

### Science

- Studied the structure of the noncommutative exceptional algebra of hypercomplex numbers with 4 units (quaternions). Proved the possibility of a vector quaternion formulation of the theory of relativity. It confirms all the predictions of Einstein's theory, but offers a symmetric (6-dimensional) structure of the model of the Universe.
- Studied the fractal structure of 3D-space - the geometric image of vector units of the quaternion algebra. Proved that the condition for the stability of algebra (and 3D-space) under the simplest deformations of a fractal subspace is precisely the Schrodinger equation – the physical equation of quantum mechanics.
- Studied methods of spacecraft control systems and calculation of space probe trajectories. Proposed a new algorithm for controlling spacecraft. Proved that the gravitational maneuver of the space probe allows to multiply the small physical effects of the deviation of bodies from the classical orbits in the Solar system.

### Scientific interests

- geometrization of physical interactions
- relationship between quaternion mathematics and the laws of physics and the structure of the Universe
- study of relativistic effects of the motion of cosmic bodies