Related papers: Primitive spherical systems
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…
New variables of separation for few integrable systems on the two-dimensional sphere with higher order integrals of motion are considered in detail. We explicitly describe canonical transformations of initial physical variables to the…
All the four giant planets in our Solar System have rings, but their characteristics are very different. The rings consist of a number of small particles, although individual particles have not been directly imaged. Near the central planet,…
Aspects of our Solar System's formation are deduced from observations of the chemical nature of matter. Massive cores are indicative of terrestrial-planet-composition-similarity to enstatite chondrite meteorites, whose highly-reduced state…
The first steps in defining tropicalization for spherical varieties have been taken in the last few years. There are two parts to this theory: tropicalizing subvarieties of homogeneous spaces and tropicalizing their closures in spherical…
Consider an analytic map of a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs of lines passing through 0 to germs of circles. Such a map is called rounding. We introduce a natural equivalence…
This chapter of the book Planetary Ring Systems addresses the origin of planetary rings, one of the least understood processes related to planet formation and evolution. Whereas rings seem ubiquitous around giant planets, their great…
SPM (Sand Pile Model) is a simple discrete dynamical system used in physics to represent granular objects. It is deeply related to integer partitions, and many other combinatorics problems, such as tilings or rewriting systems. The…
Spherical Designs are finite sets of points on the sphere $\mathbb{S}^{d}$ with the property that the average of certain (low-degree) polynomials in these points coincides with the global average of the polynomial on $\mathbb{S}^{d}$. They…
In rotating scattering systems, the generic saddle-center scenario leads to stable islands in phase space. Non-interacting particles whose initial conditions are defined in such islands will be trapped and form rotating rings. This result…
We prove some fundamental structural results for spherical varieties in arbitrary characteristic. In particular, we study Luna's two types of localization and use it to analyze spherical roots, colors and their interrelation. At the end, we…
Rings are ubiquitous around giant planets in our Solar System. They evolve jointly with the nearby satellite system. They could form either during the giant planet formation process or much later, as a result of large scale dynamical…
Spiral galaxies show axial symmetry and an intrinsic 2D-chirality. Environmental effects can influence the chirality of originally isolated stellar systems and a progressive loss of chirality can be recognised in the Hubble sequence. We…
If a (weighted) spherical design is defined as an integration (cubature) rule for a unitarily invariant space P of polynomials (on the sphere), then any unitary image of it is also such a spherical design. It therefore follows that such…
An algebraic variety is said to have the $A_k$-property if any $k$ points are contained in some common affine open neighbourhood. A theorem of W{\l}odarczyk states that a normal variety has the $A_2$-property if and only if it admits a…
This is a survey of what is known and/or conjectured about the prime and primitive spectra of quantum algebras, of quantized coordinate rings in particular. The topological structure of these spectra, their relations to classical affine…
We list combinatorial criteria of some singularities, which appear in the Minimal Model Program or in the study of (singular) Fano varieties, for spherical varieties. Most of the results of this paper are already known or are quite easy…
In this article, we introduce and study the concept of $\textit{spherical-vectors}$, which can be perceived as a natural extension of the arguments of complex numbers in the context of quaternions. We initially establish foundational…
An introduction to some basic ideas of the author's "quantum cybernetics" is given, which depicts waves and "particles" as mutually dependent system components, thus defining "organizationally closed systems" characterized by a fundamental…
A completely reducible subcomplex of a spherical building is a spherical building.