Related papers: Some simplicial complexes of universal Osborn loop…

This paper shows that orbital equations generated by iteration of polynomial maps do not have necessarily a unique representation. Remarkably, they may be represented in an infinity of ways, all interconnected by certain nonlinear…

The closed homogeneous and isotropic universe is considered. The bundles of Weyl and Dirac spinors for this universe are explicitly described. Some explicit formulas for the basic fields and for the connection components in stereographic…

In this paper we show that a simplicial complex can be determined uniquely up to isomorphism by its barycentric subdivision or comparability graph. At the end, it is summarized several algebraic, combinatorial and topological invariants of…

We state that any constant curvature Riemannian metric with conical singularities of constant sign curvature on a compact (orientable) surface $S$ can be realized as a convex polyhedron in a Riemannian or Lorentzian) space-form. Moreover…

We say that a loop is unbreakable when it does not have nontrivial subloops. While the cyclic groups of prime order are the only unbreakable finite groups, we show that nonassociative unbreakable loops exist for every order n >= 5. We…

Let $A$ and $B$ be finite-dimensional simple algebras with arbitrary signature over an algebraically closed field. Suppose $A$ and $B$ are graded by a semigroup $S$ so that the graded identitical relations of $A$ are the same as those of…

We define a suitably tame class of singular symplectic curves in 4-manifolds, namely those whose singularities are modeled on complex curve singularities. We study the corresponding symplectic isotopy problem, with a focus on rational…

We are interested in the naive problem whether we can move a solid object in a solid box or not. We restrict move to rotation. In the case we can, the centre and the ``direction'' of rotation may be restricted. Simplifying, we consider…

M\"obius transformations of the extended complex plane are at the crossroads of many interesting topics, e.g., they form a group under composition, are the simplest form of rational function, and are a path to Lie theory. Quaternionic…

It is shown that rational extensions of the isotropic Dunkl oscillator in the plane can be obtained by adding some terms either to the radial equation or to the angular one obtained in the polar coordinates approach. In the former case, the…

We give a complete classification of local and global conformal biharmonic maps between any two space forms by proving that a conformal map between two space forms is proper biharmonic if and only if the dimension is 4, the domain is flat,…

We suggest a geometrical framework to discuss periodic layered structures in the unit disk. The band gaps appear when the point representing the system approaches the unit circle. We show that the trace of the matrix describing the basic…

The symmetric group on 4 letters has the reflection group $D_{3}$ as an isomorphic image. This fact follows from the coincidence of the root systems $A_{3}$ and $D_{3}$. The isomorphism is used to construct an orthogonal basis of…

An abstract polytope of rank n is said to be chiral if its automorphism group has two orbits on the flags, such that adjacent flags belong to distinct orbits. Examples of chiral polytopes have been difficult to find. A "mixing" construction…

The symplectomorphism group of a 2-dimensional surface is homotopy equivalent to the orbit of a filling system of curves. We give a generalization of this statement to dimension 4. The filling system of curves is replaced by a decomposition…

We put in a general framework the situations in which a Riemannian manifold admits a family of compatible complex structures, including hyperkahler metrics and the Spin-rotations of arxiv:1302.2846. We determine the (polystable) holomorphic…

We show that a simply connected stable plane with connected lines is isomorphic to an open subplane of a classical projective plane (i.e., a plane over the real or complex numbers, the quaternions or the octonions) if it has that property…

In a compact orbifold, for small prescribed volume, an isoperimetric region is close to a small metric ball; in a Euclidean orbifold, it is a small metric ball.

``Quasi-elliptic'' functions can be given a ring structure in two different ways, using either ordinary multiplication, or convolution. The map between the corresponding standard bases is calculated. A related structure has appeared…

The intersection matrix of a simplicial complex has entries equal to the rank of the intersection of its facets. In [1] the authors prove the intersection matrix is enough to determine a triangulation of a surface up to isomorphism. In this…