arXiv preprints from January 1, 2026 through September 5, 2026 — 03:28:22 EST
Relative periodic orbits (RPOs) are solutions of the three-body problem that are periodic in a uniformly rotating reference frame and, in general, quasi-periodic in inertial coordinates. We present a numerical procedure for computing and continuing one-parameter families of RPOs of the planar Newtonian three-body problem. The method...
Let A denote the infinite Gram matrix associated with the standard L2 inner product of asymmetrically-weighted (AW) Hermite functions. We derive an explicit representation of its entries and its Cholesky factorization. We further show that this factorization admits a natural interpretation on a scaled Bargmann-Fock basis. An explicit...
We consider the voter model on the giant component of a hyperbolic random graph, which is a spatial scale-free network, in the sparse and linear-giant regime $α\in(1/2,1)$. We find that the quenched expected consensus time has order $n^{2-1/α}$, as the number of vertices $n\to\infty$, with probability arbitrarily close to one. This is...
We prove that a compact Kähler manifold carrying a regular Riemannian foliation whose leaves are Lagrangian and minimal is flat. In order to prove this result, we establish a foliated version of an integral formula due to Ros.
Permutative sliding block codes - in the sense of Hedlund - give rise to finite-to- one extensions of subshifts. We provide criteria under which minimality and unique ergodicity are preserved by this 'lifting procedure'. These findings are illustrated by means of some nat- ural example families, which we use to obtain strictly ergodic...
In this paper we study the motivic Chabauty--Kim method, which aims to determine the set of $S$-integral points of $\mathbb{P}^1\smallsetminus \{0,1,\infty\}$, over cyclotomic fields. We focus on the case $K=\mathbb{Q}(ζ_8)$ and $S=\left\{(1-ζ_8)\right\}$, where we obtain explicit polylogarithmic Kim functions up to depth $4$ and...
Fixed-width sequential stopping rules terminate a stochastic simulation once an estimated confidence interval reaches a prescribed width. Classical fixed-width theory typically relies on a strongly consistent estimator of the asymptotic variance. This makes the normalized stopping time asymptotically deterministic, allowing...
We develop a data-driven framework for nonlinear port-Hamiltonian (pH) systems based on interpolation conditions to characterize consistency between observed data and structured dynamical models. Specifically, we derive necessary and sufficient conditions for the existence of a pH system with a smooth (convex) Hamiltonian instantly...
This comment revisits Lemma 1 in [1], which plays a central role in the event-triggered stabilization analysis developed therein. We identify technical gaps in the proof of the lemma and provide a corrected argument. In particular, careful treatment of the exponentially decaying term shows that its decay rate must be retained in the...
This paper considers decentralized contingency MPC for multi-agent control under a state-only information pattern, with particular focus on limited sensing and plug-and-play operation. The objective is to retain recursive feasibility, safety, and Lyapunov-type convergence while reducing conservatism in local interaction handling. The...
The chiral limit of the Bistritzer--MacDonald model for twisted bilayer graphene has exactly flat bands at magic angles. We show that exact flatness can persist beyond the chiral limit with nonchiral tunnelling potentials in the usual symmetry class. We construct a family of nonchiral tunnelling potentials for which the Hamiltonian...
We study statistical manifolds $(M,g,\nabla,\nabla^{*})$ endowed with a nonzero $(1,1)$-tensor field $Θ$ satisfying the gauge equation \[ \nabla_X(ΘY)=Θ(\nabla_X^{*}Y). \] We first characterize this condition in terms of the statistical difference tensor \[ K=\nabla-\nabla^{g}. \] When $Θ$ is parallel with respect to the Levi-Civita...
This article investigates the problem of assigning multiple identical interceptors over multiple identical aerial threats, where all interceptors are launched in a single salvo. For this problem, two strategies have been studied in the literature: (A) to spread all interceptors as evenly as possible over all threats, and (B) to...
Differential privacy provides a rigorous framework for protecting private information, typically achieved by adding random noise to query results. The generalized Gaussian family is a flexible class of additive noise distributions indexed by the shape parameter $p$ and includes the Laplace and Gaussian distributions as special cases...
In this paper, we obtain a full characterization of the finite positive Borel measures $μ$ on $\mathbb D$ for which the embedding $$ \operatorname{id}:\mathcal D_{p-1}^p\longrightarrow L^p(μ),\qquad p>2, $$ is bounded. More precisely, for any dyadic system $\mathcal D$ on $\mathbb T$, we prove that this embedding is bounded if and...
In this paper, we establish a new type of stability phenomenon for the topological entropy of Hamiltonian diffeomorphisms of closed surfaces. For a closed surface endowed with an area form $(Σ,ω)$ and a Hamiltonian diffeomorphism $φ$ of $(Σ,ω)$, we show that for every $\varepsilon>0$ there exists $A=A(φ,\varepsilon)>0$ such that \[...
In this work we are concerned with the controllability of time-varying lumped control systems governed by a semilinear differential equation. We consider the semilinear system as a perturbation of a linear system. Assuming the underlying linear system is controllable, and the nonlinear forcing function satisfies a boundedness...
In this paper, we initiate the study of colored exponential random graph models (ERGMs), a class of exponential-family models for networks with multiple types of edge relations. Using the framework of probability graphons, we first derive a variational representation for the limiting free energy, whose maximizers determine the...
Polymath8b proved that $H_1 = \liminf (p_{n+1}-p_n) \leq 246$. In this paper we show how the Bombieri-Vinogradov theorem can be combined with newer equidistribution estimates for smooth moduli to obtain the improved bound $H_1 \leq 240$.
We develop two methods for proving infinite girth from boundary dynamics. First, we use topologically free extreme boundary actions to give a boundary-dynamical proof of infinite girth for finitely generated acylindrically hyperbolic groups. The second combines Nakamura's criterion with, respectively, flag-space and Roller-boundary...
We prove that when the J-equation does not admit a smooth solution, there is always only a finite number of obstructing optimally destabilizing curves and divisors on compact Kähler manifolds of any dimension. For threefolds, this establishes the unconditional finiteness of all optimally destabilizing subvarieties. We moreover...
The work introduces the novel Dunkl two-photon and Dunkl-Schrödinger algebras as reflection-extended counterparts of the standard six-dimensional two-photon and Schrödinger algebras. These extensions are realized through the presence of an involutive generator representing a reflection, and they reduce to the undeformed two-photon and...
We construct, for every even $n \ge 2$, a positive cone on $F_n \times \mathbb{Z}$ that is finitely generated as a semigroup, extending the previously known construction for $n = 2$. Malicet, Mann, Rivas and Triestino proved that $F_n \times \mathbb{Z}$ admits an isolated left-order if and only if $n$ is even. Since every finitely...
We determine the exact dimensional range in which a normalized longest signed sum, which we call a Bang vector, always satisfies the real polarization inequality: this prescription is universally valid if and only if \(n\leq 14\). For every \(n\geq 15\) we construct \(n\) unit vectors whose all-positive sum is, up to global sign, the...
We investigate the fake stationarity properties of solutions to forward Stochastic Volterra Integral Equations (SVIEs) with affine drift and long-memory (regular) kernels, both on finite horizons and in the long-run regime. By either deriving explicit closed-form specifications for the deterministic initial condition $φ$ and the...