Related papers: Pseudo Unique Sink Orientations
We study the closure $\bar{CSO}$ of the set $CSO$ of all complex symmetric operators on a separable, infinite-dimensional, complex Hilbert space. Among other things, we prove that every compact operator in $\bar{CSO}$ is complex symmetric.…
There are only 10 Euclidean forms, that is flat closed three dimensional manifolds: six are orientable and four are non-orientable. The aim of this paper is to describe all types of $n$-fold coverings over orientable Euclidean manifolds…
It was recently demonstrated that two-dimensional Townes solitons (TSs) in two-component systems with cubic self-focusing, which are normally made unstable by the critical collapse, can be stabilized by linear spin-orbit coupling (SOC), in…
We introduce a construction of pseudo-Anosov homeomorphisms on n-times punctured spheres and surfaces with higher genus using only sufficiently many positive half-twists. These constructions can produce explicit examples of pseudo-Anosov…
A pseudo-edge graph of a convex polyhedron K is a 3-connected embedded graph in K whose vertices coincide with those of K, whose edges are distance minimizing geodesics, and whose faces are convex. We construct a convex polyhedron K in…
We present a study of cubic surfaces from the novel perspective of positive geometry. Our positive geometries have dimension two (the surface minus its 27 lines), dimension three (its complement in 3-space), and dimension four (the moduli…
We study a system of equal-sized circular discs each with an asymmetrically placed pivot at a fixed distance from the center. The pivots are fixed at the vertices of a regular triangular lattice. The discs can rotate freely about the…
The quasi-degeneracy between the single-particle states $(n,\,l,\,j=l+1/2)$ and $(n-1,\,l+2,\,j=l+3/2)$ indicates a special and hidden symmetry in atomic nuclei---the so-called pseudospin symmetry (PSS)---which is an important concept in…
We give a complete deformation classification of real Zariski sextics, that is of generic apparent contours of nonsingular real cubic surfaces. As a by-product, we observe a certain "reversion" duality in the set of deformation classes of…
A complete set of N+1 mutually unbiased bases (MUBs) forms a convex polytope in the N^2-1 dimensional space of NxN Hermitian matrices of unit trace. As a geometrical object such a polytope exists for all values of N, while it is unknown…
The number of planar Eulerian maps with n edges is well-known to have a simple expression. But what is the number of planar Eulerian orientations with n edges? This problem appears to be difficult. To approach it, we define and count…
This paper introduces the notion of second minimal $n$-periodic orbit of the continuous map on the interval according as if $n$ is a successor of the minimal period of the map in Sharkovski ordering. We pursue classification of second…
This work presents UNO, a unified monocular visual odometry framework that enables robust and adaptable pose estimation across diverse environments, platforms, and motion patterns. Unlike traditional methods that rely on deployment-specific…
We argue that with the discovery of neutrino mass effects at Super-Kamiokande there is a clear logical chain leading from the Standard Model through the MSSM and the recently developed Minimal Left Right Supersymmetric models with a…
We describe an algorithm which, given two essential curves on a surface $S$, computes their distance in the curve graph of $S$, up to multiplicative and additive errors. As an application, we present an algorithm to decide the…
A graph G is said to be 1-perfectly orientable (1-p.o. for short) if it admits an orientation such that the out-neighborhood of every vertex is a clique in G. The class of 1-p.o. graphs forms a common generalization of the classes of…
A cube is an 8-rep-tile: it is the union of eight smaller copies of itself. Is there a set with a hole which has this property? The computer found an interesting and complicated solution, which then could be simplified. We discuss some…
Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous application focused on two-dimensional homogeneous fluid, this study examines the geometric…
The point-pushing subgroup P(S) of the mapping class group Mod(S) of a surface with marked point is an embedding of \pi_1(S) given by pushing the marked point around loops. We prove that for g>=3, the subgroup P(S) is the unique normal,…
There exists a bijection between the configuration space of a linear pentapod and all points $(u,v,w,p_x,p_y,p_z)\in\mathbb{R}^{6}$ located on the singular quadric $\Gamma: u^2+v^2+w^2=1$, where $(u,v,w)$ determines the orientation of the…