Related papers: Solitaire: Recent Developments
In this paper we are interested in the {\it{Cage Problem}} that consists in constructing regular graphs of given girth $g$ and minimum order. We focus on girth $g=5$, where cages are known only for degrees $k \le 7$. We construct regular…
This paper aims to find new explicit solutions including multi-soliton, multi-positon, multi-negaton, and multi-periodic for a coupled Volterra lattice system which is an integrable discrete version of the coupled KdV equation. The…
Research Briefs: Singularity Avoidance in Canonical Quantum Gravity, by Viqar Husain What's New in LIGO, by David Shoemaker Conference reports: Scanning New Horizons: GR Beyond 4 dimensions, by Donald Marolf Quantum Gravity in the Americas…
This is a brief survey of recent results related to austere submanifolds, mainly based on the papers [24,25].
We consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions we show that wave-like solutions exist when obstacles (characterized by "holes") are present in the…
The Generalized Sliding-Tile Puzzle (GSTP), allowing many square tiles on a board to move in parallel while enforcing natural geometric collision constraints on the movement of neighboring tiles, provide a high-fidelity mathematical model…
This paper presents new efficient solutions to the rolling shutter camera absolute pose problem. Unlike the state-of-the-art polynomial solvers, we approach the problem using simple and fast linear solvers in an iterative scheme. We present…
We introduce a new class of billiard systems in the plane, with boundaries formed by finitely many arcs of confocal conics such that they contain some reflex angles. Fundamental dynamical, topological, geometric, and arithmetic properties…
These notes briefly discuss Fourier transforms of finite measures and extensions of Fourier integrals to points in complex domains.
Recently, very interesting results have been obtained concerning the Fourier spectra of power permutations over a finite field. In this note we survey the recent ideas of Aubry, Feng, Katz, and Langevin, and we pose new open problems…
Monotone inclusion problems occur in many areas of optimization and variational analysis. Splitting methods, which utilize resolvents or proximal mappings of the underlying operators, are often applied to solve these problems. In 2022,…
In recent years, the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers (SUNDIALS) has been redesigned to better enable the use of application-specific and third-party algebraic solvers and data structures. Throughout this work,…
Contents: Editorial Correspondents News: - Topical Group News, by Jim Isenberg - We hear that..., by Jorge Pullin - The Chandra Satellite, by Beverly Berger Research Briefs: - Analytical event horizons of merging black holes, by Simonetta…
In this survey we give a brief introduction to, and review the progress made in the last decade in understanding the geometry of the moduli spaces A_g of principally polarized abelian varieties and its compactifications. Topics surveyed…
The problem of the existence of an analytic normal form near an equilibrium point of an area-preserving map and analyticity of the associated coordinate change is a classical problem in dynamical systems going back to Poincar\'e and Siegel.…
In this paper we give a short survey of recent results on algebraic version of the Birkhoff conjecture for integrable billiards on surfaces of constant curvature. We also discuss integrable magnetic billiards. As a new application of the…
RecBole has recently attracted increasing attention from the research community. As the increase of the number of users, we have received a number of suggestions and update requests. This motivates us to make some significant improvements…
Abalone is a 2-player board game with perfect information. The game is played on a 5x5x5 hexagonal grid and ends when a player pushes 6 of their opponents' pieces off the board. Abalone is similar to games like chess and Go in that all…
We review the progress made on bounding the number of independent sets in $d$-regular and irregular graphs over the last 31 years. We particularly focus on contributions from Kahn, Zhao, and Sah et al. in incrementally proving stronger and…
We present a series of recent results on the well-posedness of very singular parabolic stochastic partial differential equations. These equations are such that the question of what it even means to be a solution is highly non-trivial. This…