Related papers: Mechanical Equations on Bi-Para Conformal Geometry
This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks.…
This document is an introduction to and review of two-dimensional mathematical physics. The reader is introduced to the subject matter primarily through problems, which are presented along with detailed worked solutions. For each chapter,…
In this paper, we develop a cohomology theory of a left-symmetric conformal algebra and study its some applications. We define the cohomology of a left-symmetric conformal algebra, and then give an isomorphism between the cohomology spaces…
Complete complex parabolic geometries (including projective connections and conformal connections) are flat and homogeneous. This is the first global theorem on parabolic geometries.
Absolute parallelism (AP) geometry is frequently used for physical applications. Although it is wider than Riemannian geometry, it has two main defects. The first is that its path equation does not represent physical trajectories of any…
Some intensive observables of the electronic ground state in condensed matter have a geometrical or even topological nature. In this Review I present the geometrical observables whose expression is known in a full many-body framework,…
Basic facts and definitions of conformal moduli of rings and quadrilaterals are recalled. Some computational methods are reviewed. For the case of quadrilaterals with polygonal sides, some recent results are given. Some numerical…
This survey is on recent advancements in the intersection of physical modeling and machine learning. We focus on the modeling of nonlinear systems which are closer to electric motors. Survey on motor control and fault detection in operation…
We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on…
We present examples of Lax-integrable multi-dimensional systems of partial differential equations with higher local symmetries. We also consider Lagrangian deformations of these equations and construct variational bivectors on them.
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 presented. Geometrical interpretations are given.
We argue here that, as it happens in Classical and Quantum Mechanics, where it has been proven that alternative Hamiltonian descriptions can be compatible with a given set of equations of motion, the same holds true in the realm of…
In this review paper, we consider three kinds of systems of differential equations, which are relevant in physics, control theory and other applications in engineering and applied mathematics; namely: Hamilton equations, singular…
We discuss computability and computational complexity of conformal mappings and their boundary extensions. As applications, we review the state of the art regarding computability and complexity of Julia sets, their invariant measures and…
These notes follow my articles [1, 6], and give some new important details. We propose here a new combinatorial method of encoding of measure spaces with measure preserving transformations, (or groups of transformations) in order to give…
Conformal invariance plays a significant role in many areas of Physics, such as conformal field theory, renormalization theory, turbulence, general relativity. Naturally, it also plays an important role in geometry: theory of Riemannian…
The duality triads were defined in the preceding paper.(ArXiv: math.GM/0402260 v 1 Feb. 2004). Notation, enumeration of formulas and references is therefore to be continued hereby. In this paper Fibonomial triangle and further Pascal-like…
In this paper we make a detailed and self-contained study of the conformalGauss map. Then, starting from the seminal work of R. Bryant and the notion of conformal Gauss map, we recover many fundamental properties of Willmore surfaces. We…
A new functional model for pairs of commuting isometries is described. Intertwining operators between such models are then studied in order to approach the classification of invariant subspaces of such pairs.
A new type of elasticity of random (multifractal) structures is suggested. A closed system of constitutive equations is obtained on the basis of two proposed phenomenological laws of reversible deformations of multifractal structures. The…