15 citations · 85 across the 32 of their papers we have counts for
34 papers
Note on star-triangle equivalence in conducting networks
E. Paal, M. Umbleja
By using the discrete Poisson equations the star-triangle (external) equivalence in conducting networks is considered and the Kennelly famous transformation formulae [Kennelly A E…
Note on homological modeling of the electric circuits
Eugen Paal, Märt Umbleja
Based on a simple example, it is explained how the homological analysis may be applied for modeling of the electric circuits. The homological branch, mesh and nodal analyses are pr…
The operadic modeling of gauge systems of the Yang-Mills type
Eugen Paal
The basics of operadic variational formalism is presented which is necessary when modeling the operadic systems. A general gauge theoretic approach to the abstract operads, based o…
Quantum counterparts of 3d Lie algebras over harmonic oscillator
E. Paal, J. Virkepu
Operadic Lax representations for the harmonic oscillator are used to construct the quantum counterparts of 3d real Lie algebras. The Jacobians of the corresponding quantum algebras…
Dynamical deformations of three-dimensional Lie algebras in Bianchi classification over the harmonic oscillator
Eugen Paal, Jyri Virkepu
Operadic Lax representations for the harmonic oscillator are used to construct the dynamical deformations of three-dimensional (3D) real Lie algebras in the Bianchi classification.…
3D binary anti-commutative operadic Lax representations for harmonic oscillator
Eugen Paal, Jyri Virkepu
It is explained how the time evolution of the operadic variables may be introduced by using the operadic Lax equation. The operadic Lax representations for the harmonic oscillator…