Related papers: Bicomplex Mobius Transformation
The arithmetic function of two variables is defined. Some properties of the function are given along with the formula that is an analog of the so-called Mobius' inversion formula. A heuristic statement is suggested.
Parabolic bifurcations in one complex dimension demonstrate a wide variety of interesting dynamical phenomena. In this paper we consider parabolic bifurcations of families of diffeomorphisms in two complex dimensions. Specifically we…
This paper is a compact overview of the heuristic approach to the recently elaborated octonionic binocular mobilevision.
Bifurcation with symmetry is considered in the case of an isotropy subgroup with a two-dimensional fixed point subspace and non-zero quadratic terms. In general, there are one or three branches of solutions, and five qualitatively different…
A discrete complexified quaternion Fourier transform is introduced. This is a generalization of the discrete quaternion Fourier transform to the case where either or both of the signal/image and the transform kernel are complex…
A bilinear formulation for the supersymmetric two-boson equation is derived. As applications, some solutions are calculated for it. We also construct a bilinear Backlund transformation.
We give some details of a simpler definition of mixed Hodge modules which has been announced in some papers. Compared with earlier arguments, this new definition is simplified by using Beilinson's maximal extension together with stability…
In this article, we study coupled fixed point theorems in newly appeared JS-metric spaces. It is important to note that the class of JS-metric spaces includes standard metric space, dislocated metric space, b-metric space etc. The purpose…
The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous…
The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…
The electromagnetic fields of the hybrid modes of an optical fiber are reformulated using bi-complex mathematics, which leads to simpler expressions relative to those found with the widely used, conventional complex formulation. Generalized…
A method to define the complex structure and separate the conformal mode is proposed for a surface constructed by two-dimensional dynamical triangulation. Applications are made for surfaces coupled to matter fields such as $n$ scalar fields…
We present identities for permutations with fixed points. The formulas are based on successive derivations or integrations of the determinant of a particular matrix.
In this paper, considering a wider class of simulation functions some fixed point results for multivalued mappings in $\alpha$-complete metric spaces have been presented. Results obtained in this paper extend and generalize some well-known…
We study a dynamical counterpart of bifurcation to invariant torus for a system of interconnected fast phase variables and slowly varying parameters. We show that in such a system, due to the slow evolution of parameters, there arise…
The first aim of this paper is to examine some important properties of soft metric spaces. Second is to introduce soft continuous mappings and investigate properties of soft continuous mappings. Third is to prove some fixed point theorems…
In this paper we examine the structure of complex points of real 4-manifolds embedded into complex 3-manifolds up to isotopy. We show that there are only two types of complex points up to isotopy and as a consequence, show that any such…
This article presents some computations for a new topological invariant for foliations introduced some years ago by the author using techniques from noncommutative geometry, in particular the pairing between K-Theory and cyclic cohomology.…
New invariants for 2-dimensional cell complexes are defined, which can be interpreted as curvature bounds. These invariants are proved to be rational and computable in a companion article. This document is a survey that collects theorems…
It has long been known that the ellipse normally used to model the phase space extension of a beam in linear dynamics may be represented by a complex number which can be interpreted similarly to a complex impedance in electrical circuits,…