Related papers: Radix form in hyperbolic and dual numbers
We study the relationship between multiplicative 2-forms on Lie groupoids and linear 2-forms on Lie algebroids, which leads to a new approach to the infinitesimal description of multiplicative 2-forms and to the integration of twisted Dirac…
We discuss the most elementary properties of the hyperbolic trigonometry and show how they can be exploited to get a simple, albeit interesting, geometrical interpretation of the special relativity. It yields indeed a straightforword…
We suggest a new approach to the study of relatively hyperbolic groups based on relative isoperimetric inequalities. Various geometric, algebraic, and algorithmic properties are discussed.
The frequencies and linewidths of spin waves in a two-dimensional periodic superlattice of magnetic materials are found, using the Landau-Lifshitz-Gilbert equations. The form of the exchange field from a surface-torque-free boundary between…
We study the arithmetic codings of hyperbolic automorphisms of the 2-torus, i.e. the continuous mappings acting from a certain symbolic space of sequences with a finite alphabet endowed with an appropriate structure of additive group onto…
We explore the hyperbolic structure of the RNS formulation of perturbative superstring theory. The aim is to provide a systematic method to explicitly compute on-shell and off-shell closed superstring amplitudes with an arbitrary number of…
We study existence, uniqueness, and distributional aspects of generalized solutions to the Cauchy problem for first-order symmetric (or Hermitian) hyperbolic systems of partial differential equations with Colombeau generalized functions as…
Three hyperbolic type metrics including the triangular ratio metric, the $j^*$-metric and the M\"obius metric are studied in an annular ring. The Euclidean midpoint rotation is introduced as a method to create upper and lower bounds for…
New types of magnetic structures in the Heisenberg model are found. Analytical methods are used to describe spiral structures, spiral vortex structures, and their interaction. Methods for obtaining these structures in real systems,…
The paper is devoted to hyperbolic (generally speaking, non-Lagrangian and nonlinear) partial differential systems possessing a full set of differential operators that map any function of one independent variable into a symmetry of the…
The theory of symmetric-hyperbolic systems is useful for constructing smooth solutions of nonlinear wave equations, and for studying their singularities, including shock waves. We present the main techniques which are required to apply the…
A description of Lagrangian and Hamiltonian formalisms naturally arisen from the invariance structure of given nonlinear dynamical systems on the infinite--dimensional functional manifold is presented. The basic ideas used to formulate the…
We present an infinite dimensional Banach space in which the set of hyperbolic linear isomorphisms in that space is not dense (in the norm topology) in the set of linear isomorphisms.
A study is made of real Lie algebras admitting a hypersymplectic structure, and we provide a method to construct such hypersymplectic Lie algebras. We use this method in order to obtain the classification of all hypersymplectic structures…
Generally the study of algebraic deals with the concepts like groups, semigroups, groupoids, loops, rings, near-rings, semirings and vector spaces. The study of bialgebraic structures deals with the study of bistructures like bigroups,…
This survey article describes the algorithmic approaches successfully used over the time to construct hyperbolic structures on 3-dimensional topological "objects" of various types, and to classify several classes of such objects using such…
Canonical matrices are given for (a) bilinear forms over an algebraically closed or real closed field; (b) sesquilinear forms over an algebraically closed field and over real quaternions with any nonidentity involution; and (c) sesquilinear…
We investigate the (linearized) Morse index of solutions to Hamiltonan systems, with a focus on convex Hamiltonians functions and sign-changing radial solutions. For strongly coupled systems, we describe the profile of the radial solutions…
The engineering of specialty lasers with unconventional mode structures is one of the modern challenges in the development of integrated coherent sources. Examples include the use of bound states in the continuum, microlasers with orbital…
We survey several methods of extending quasisymmetric homeomorphisms of the real line to bi-Lipschitz diffeomorphisms of the upper half-plane with respect to the hyperbolic metric.