Related papers: Central Configurations Formed By Two Twisted Regul…
A spectral sequence calculating the homology groups of some spaces of maps equivariant under compact group actions is described. For the main example, we calculate the rational homology groups of spaces of even and odd maps $S^m \to S^M$,…
We study the geometric structure of the statistical models for two-by-two contingency tables. One or two odds ratios are fixed and the corresponding models are shown to be a portion of a ruled quadratic surface or a segment. Some pointers…
The geometrical description of deformation quantization based on quantum duality principle makes it possible to introduce deformed Lie-Poisson structure. It serves as a natural analogue of classical Lie bialgebra for the case when the…
We introduce multi-soliton sets in the two-dimensional medium with the second-harmonic-generating nonlinearity subject to spatial modulation in the form of a triangle of singular peaks. Various families of symmetric and asymmetric sets are…
The hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement. The $n$-dimensional twisted cube, denoted by $TQ_n$, an important variation of the hypercube, possesses some…
We present a computer assisted proof of the full listing of central configurations for spatial n-body problem for n = 5 and 6, with equal masses. For each central configuration we give a full list of its euclidean symmetries. For all masses…
An n-simplex is said to be n-well-centered if its circumcenter lies in its interior. We introduce several other geometric conditions and an algebraic condition that can be used to determine whether a simplex is n-well-centered. These…
We consider the planar two-center problem for a convex polygon: given a convex polygon in the plane, find two congruent disks of minimum radius whose union contains the polygon. We present an $O(n\log n)$-time algorithm for the two-center…
In his paper "Shapes of Polyhedra and Triangulations of the Sphere", Thurston found that the set of shapes of convex polyhedra with prescribed cone-deficits has a complex hyperbolic structure. Inspired by his work, this paper studies the…
We study the geometric structure of Poncelet $n$-gons from a projective point of view. In particular we present explicit constructions of Poncelet $n$-gons for certain $n$ and derive algebraic characterisations in terms of bracket…
The parameter space of $n$ ordered points in projective $d$-space that lie on a rational normal curve admits a natural compactification by taking the Zariski closure in $(\mathbb{P}^d)^n$. The resulting variety was used to study the…
Let $(G,N)$ be a pair of groups. In this article, first we construct a relative central extension for the pair $(G,N)$ such that special types of covering pair of $(G,N)$ are homomorphic image of it. Second, we show that every perfect pair…
Central configurations are solutions of the equations $\lambda m_j\boldsymbol{q}_j = \frac{\partial U}{\partial \boldsymbol{q}_j}$, where $U$ denotes the potential function and each $\boldsymbol{q}_j$ is a point in the $d$-dimensional…
We establish the existence of a single-parameter family of the concave kite central configurations in the 4-body problem with two pairs of equal masses. In such configurations, one pair of the masses must lie on the base of an isosceles…
We review the basic ideas lying at the foundation of the recently developed theory of twisted symmetries of differential equations, and some of its developments.
Twisted links are a generalization of classical links and correspond to stably equivalence classes of links in thickened surfaces. In this paper we introduce twisted intersection colorings of a diagram and construct two invariants of a…
The configuration of a homothetic motion in the N-body problem is called a central configuration. In this paper, we prove that there are exactly three planar non-collinear central configurations for masses x, -x, y, -y with x different from…
The diagonals of a quadrilateral form four component triangles (in two ways). For each of various shaped quadrilaterals, we examine 1000 triangle centers located in these four component triangles. Using a computer, we determine when the…
In supersymmetric theories, protected quantities can be reorganized into holomorphic-topological theories by twisting. Recently, it was observed by Jonsson, Kim and Young that residual super-Poincar\'e symmetries in certain twisted theories…
Four-manifold theory is employed to study the existence of (twisted) generalized complex structures. It is shown that there exist (twisted) generalized complex structures that have more than one type change loci. In an example-driven…