Related papers: On the ternary complex analysis and its applicatio…
We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is…
We develop the properties of the $n$-th sequential topological complexity $TC_n$, a homotopy invariant introduced by the third author as an extension of Farber's topological model for studying the complexity of motion planning algorithms in…
We investigate circularly symmetric static solutions in three-dimensional gravity with a minimally coupled massive scalar field. We integrate numerically the field equations assuming asymptotic flatness, where black holes do not exist and a…
The goal of this thesis is the search for integrable and superintegrable systems with magnetic field. We formulate the quantum mechanical determining equations for second order integrals of motion in the cylindrical coordinates and we find…
We define a relation that describes the ternary commutator for congruence modular varieties. Properties of this relation are used to investigate the theory of the higher commutator for congruence modular varieties.
The paper proposes a vector generalization of the basic concepts of the theory of complex variable: the concept of modulus and argument of complex number. The author introduces some generalizations of the notion of holomorphic functions and…
We discuss an unusual phenomenon in (integral) positive ternary quadratic forms. We also describe an interesting pairing of genera of ternary forms.
We introduce a mixed-state generalization of the multi-entropy through the canonical purification, which we call reflected multi-entropy. We propose the holographic dual of this measure. For the tripartite case, a field-theoretical…
The theory of slice regular functions of a quaternion variable is applied to the study of orthogonal complex structures on domains \Omega\ of R^4. When \Omega\ is a symmetric slice domain, the twistor transform of such a function is a…
This short note introduces a geometric representation for binary (or ternary) sequences. The proposed representation is linked to multivariate data plotting according to the radar chart. As an illustrative example, the binary Hamming…
A new method for derivation of the equation of motion from the field equation is proposed. The problem of embedding the singularities in a field satisfying the field equations is discussed.
In this study, the properties of an oscillating system composed of a pendulum connected to a seesaw and placed on a moving platform with a certain slope are analyzed. Using complex numbers to collect the information contained in the system…
An expression for a third-order link integral of three magnetic fields is presented. It is a topological invariant and therefore an invariant of ideal magnetohydrodynamics. The integral generalizes existing expressions for third-order…
In this paper, we give a survey of the known results concerning the tensor rank of the multiplication in finite extensions of finite fields, enriched with some not published recent results as well as analyzes enhancing the qualitative…
The trinomial transform of a sequence is a generalization of the well-known binomial transform, replacing binomial coefficients with trinomial coefficients. We examine Pascal-like triangles under trinomial transform, focusing on the ternary…
Results of a general study on the dynamics of cosmological scalar fields with arbitrary potentials are presented. Exact and approximate attractor solutions are found, with applications to quintessence, moduli stabilization and inflation.
The development of the theory of three-dimensional harmonic mappings is considered. The new classes of mappings that generate three-dimensional harmonic functions are introduced. The physical interpretation of these mappings is applied to…
The behavior of spinning particles in the stationary homogeneous electric field is considered and trajectories are found for various spin orientations. We study the acceleration of spinning particles by an electric field, as well as the…
In this work we investigate lump-like solutions in models described by a single real scalar field. We start considering non-topological solutions with the usual lump-like form, and then we study other models, where the bell-shape profile…
The factorization technique for superintegrable Hamiltonian systems is revisited and applied in order to obtain additional (higher-order) constants of the motion. In particular, the factorization approach to the classical anisotropic…