Related papers: Images of circles, lines, balls and half-planes un…
This paper surveys some results and methods in topological transformation groups.
Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.
This work is devoted to study the deformation of spacetime metrics as generalized conformal transformations. Some applications are also considered, in particular the equations of motion in deformed spacetime are studied.
M\"obius transformations have been studied over the field of complex numbers. In this paper, we investigate M\"obius transformations over two rings which are not fields: the ring of double numbers and the ring of dual numbers. We give types…
We provide a description of W_3 transformations in terms of deformations of convex curves in two dimensional Euclidean space. This geometrical interpretation sheds some light on the nature of finite W_3-morphisms. We also comment on how…
Properties and examples of the dual transformation between two planes, which is such that the coordinates of a point in the original plane give the coefficients of a line in the dual plane and the coefficients of a line in the original…
Having been studied since long by statisticians, multivariate median concepts found their way into the image processing literature in the course of the last decades, being used to construct robust and efficient denoising filters for…
We present a review of nonequilibrium phase transitions in mass-transport models with kinetic processes like fragmentation, diffusion, aggregation, etc. These models have been used extensively to study a wide range of physical problems. We…
This paper focus on the theoretical analysis and simulation of electromagnetic wave transforms, which is widely encountered in teaching physics. When the electromagnetic wave is not consistent with the shape of the object, it is often…
Circularly polarized Gauss-Laguerre GL(0,0) and GL(0,1) laser beams that cross at their waists at a small angle are shown to generate a quasi-paraxial field that contains an axial line of circular polarization, a C line, surrounded by…
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…
In this paper, we mainly focus on formal deformation theory of module homomorphisms. We first introduce the cohomology of module homomorphisms and study formal one-parameter deformation. We obtain some properties about obstructions. Then we…
This is an experimental case study in real algebraic geometry, aimed at computing the image of a semialgebraic subset of 3-space under a polynomial map into the plane. For general instances, the boundary of the image is given by two highly…
The article provides a brief survey of the mathematics of some of the newly being developed so called "hybrid" (also called "multi-physics" or "multi-wave") imaging techniques.
We show that conformal transformations on the generalized Minkowski space $\mathbb{R}^{p,q}$ map hyperboloids and affine hyperplanes into hyperboloids and affine hyperplanes. We also show that this action on hyperboloids and affine…
In this paper, we study how certain vector bundles on an elliptic surface are changed under logarithmic transformations.
The paper is devoted to the study of homeomoephisms with finite distortion on the plane with use of the modulus techniques.
In this survey article, we summarise the known results towards the conjecture: elliptic curves over totally real number fields are modular. For understanding these recent results in the literature, we present some necessary background along…
We study Mazur rotations problem focusing on the metric aspects of the action of the isometry group and semitransitivity properties.
Unitary rotations of polychromatic images on finite two-dimensional pixellated screens provide invertibility, group composition, and thus conservation of information. Rotations have been applied on monochromatic image data sets, where we…