Related papers: Bulgarian Solitaire: A new representation for dept…
Let n_n(C) be the algebra of strictly upper-triangular n x n matrices over the field of complex numbers and X_2 the subset of matrices of nilpotent order 2. Let B_n(C) be the group of invertible upper-triangular matrices acting on n_n(C) by…
Pulsar timing arrays (PTAs) can detect the low-frequency stochastic gravitational-wave background (GWB) generated by an ensemble of supermassive black hole binaries (BHBs). Accurate determination of BHB merger timescales is essential for…
We examine a Chern-Simons matrix model which we propose as a toy model for studying the quantum nature of black holes in 2+1 gravity. Its dynamics is described by two $N\times N$ matrices, representing the two spatial coordinates. The model…
The purpose of this note is to prove the existence of a remarkable structure in an iterated sumset derived from a set $P$ in a Cartesian square $\mathbb{F}_p^n\times\mathbb{F}_p^n$. More precisely, we perform horizontal and vertical sums…
We analyze the known results for the eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation in the perturbative regime using the analytic continuation of harmonic sums from even positive arguments to the complex plane. The…
We derive a continuous family of virial identities for O($n$) symmetric configurations, parameterized by an exponent $\alpha$ that controls the radial weighting. The family provides a systematic decomposition of the global constraint into…
We introduce a one-dimensional system combining the $\mathcal{PT}$-symmetric complex periodic potential and the $\chi ^{(2)}$ (second-harmonic-generating) nonlinearity. The imaginary part of the potential, which represents spatially…
We study the general equations determining BPS Black Holes by using a Solvable Lie Algebra representation for the homogenous scalar manifold U/H of extended supergravity. In particular we focus on the N=8 case and we perform a general group…
Black hole solutions of supergravity theories form families that realizing the deep nonlinear "duality" symmetries of these theories. They form orbits under the action of these symmetry groups, with extremal (i.e. BPS) solutions at the…
Dynamical billiards, or the behavior of a particle traveling in a planar region $D$ undergoing elastic collisions with the boundary, has been extensively studied and is used to model many physical phenomena such as a Boltzmann gas. Of…
Dense stellar clusters are natural sites for the origin and evolution of exotic objects such as relativistic binaries (potential gravitational wave sources), blue stragglers, etc. We investigate the secular dynamics of a binary system…
In a previous escapade we gave a collection of continued fractions involving Catalan's constant. This paper provides more general formulae governing those continued fractions. Having distinguished different cases associated to regions in…
In this exploratory study, we demonstrate the capability of the numerical-relativity code BAM to simulate fully relativistic black-hole binary-single and binary-binary encounters. While previous work has demonstrated the general capability…
In symmetric groups, studies of permutation factorizations or triples of permutations satisfying certain conditions have a long history. One particular interesting case is when two of the involved permutations are long cycles, for which…
Simple formulas for the number of different cyclic and dihedral necklaces containing $n_j$ beads of the $j$-th color, $j\leq m$ and $\sum_{j=1}^mn_j=N$, are derived.
A study of the quantum triangular billiard requires consideration of a boundary value problem for the Green's function of the Laplacian on a trianglar domain. Our main result is a reformulation of this problem in terms of coupled…
Binary black hole systems in the pre-coalescence stage are numerically constructed by demanding that the associated spacetime admits a helical Killing vector. Comparison with third order post-Newtonian calculations indicates a rather good…
We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed…
Let $G=G_{n}=GL(n)$ be the $n\times n$ complex general linear group and embed $G_{n-1}=GL(n-1)$ in the top left hand corner of $G$. The standard Borel subgroup of upper triangular matrices $B_{n-1}$ of $G_{n-1}$ acts on the flag variety of…
We continue the study of separable elements in finite Weyl groups. These elements generalize the well-studied class of separable permutations. We show that the multiplication map $W/U \times U \to W$ is a length-additive bijection, or…