Related papers: Coordinates based on a magnetic mirror field
Many techniques in harmonic analysis use the fact that a continuous object can be written as a sum (or an intersection) of dyadic counterparts, as long as those counterparts belong to an adjacent dyadic system. Here we generalize the notion…
Magnetic winding is a fundamental topological quantity that underpins magnetic helicity and measures the entanglement of magnetic field lines. Like magnetic helicity, magnetic winding is also an invariant of ideal magnetohydrodynamics. In…
We introduce a geometric construction which relates to the pentagram map much in the way that a logarithmic spiral relates to a circle. After introducing the construction, we establish some basic geometric facts about it, and speculate on…
Do object part localization methods produce bilaterally symmetric results on mirror images? Surprisingly not, even though state of the art methods augment the training set with mirrored images. In this paper we take a closer look into this…
Topological textures in magnetically ordered materials are important case studies for fundamental research with promising applications in data science. They can also serve as photonic elements to mold electromagnetic fields endowing them…
In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.
Classical mechanics and geometrical optics are deeply connected with each other. In this work, we generalize the analogy between these two disciplines to relativistic conditions. Using this analogy, we are able to make light follow the…
We obtain the value of the mirror magnetic field during different stages of cosmological evolution. We consider the magnetic field generation in the radiation-dominated era and the post-recombination epoch. We also estimate its galactic…
We present a topological method of obtaining the existence of infinite number of symmetric periodic orbits for systems with reversing symmetry. The method is based on covering relations. We apply the method to a four-dimensional reversible…
Magnetic fields are observed not only in stars, but in galaxies, clusters, and even high redshift Lyman-alpha systems. In principle, these fields could play an important role in structure formation and also affect the anisotropies in the…
The initial descriptions of the FITS format provided a simplified method for describing the physical coordinate values of the image pixels, but deliberately did not specify any of the detailed conventions required to convey the complexities…
Magnetic fields have been found to have an inherent capability of acting against gravity. An important question posed in the literature is whether presence of a magnetic field can alter the dynamics of a gravitational collapse and prevent…
We apply the supersymmetry approach to one-dimensional quantum systems with spatially-dependent mass, by including their ordering ambiguities dependence. In this way we extend the results recently reported in the literature. Furthermore, we…
The quaternion spaces can be used to describe the property of electromagnetic field and gravitational field. In the quaternion space, some coordinate transformations can be deduced from the feature of quaternions, including Lorentz…
A construction of polytopes is given based on integers. These geometries are constructed through a mapping to pure numbers and have multiple applications, including statistical mechanics and computer science. The number form is useful in…
We show that an appropriate generalization of the oriented area function is a perfect Morse function on the space of three-dimensional configurations of an equilateral polygonal linkage with odd number of edges. Therefore cyclic equilateral…
Several local elliptic coordinates are used to build a new polyelliptic coordinate system which is orthogonal and admits the separation of variables. Such coordinate systems can give the exact solutions of some unsolved problems in quantum…
In a large range of physics and space experiments, the direction of the magnetic field needs to be determined with an accuracy on the level of one milli radian or better. We have proposed a new type of magnetic compass - a rotation-based…
It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper, we announce an explicit formula of the Morse index for the signed area of a cyclic configuration. It depends…
The goal of this paper is to make the vertex operator algebra approach to mirror symmetry accessible to algebraic geometers. Compared to better-known approaches using moduli spaces of stable maps and special Lagrangian fibrations, this…