arXiv preprints from January 1, 2026 through September 21, 2026 — 19:42:28 EST
Böhm metrics on $S^{k+1}\times S^l$ and $S^{k+l+1}$ ($k,l\geqslant 2$, $k+l\leqslant 8$) occur in sequences of Einstein metrics that converge to a cone. We prove that, along such a sequence, the number of negative eigenvalues of the Lichnerowicz Laplacian acting on transverse-traceless tensors tends to infinity: these metrics become...
The huge amount of literature about the divergence equation in bounded Lipschitz domains of $\R^n$ ($n\ge2$) is fairly disconnected and even apparently simple problems remain unsolved. We go several steps further in the knowledge of this equation and of some related inequalities. We prove that among its infinitely many solutions there...
We study steady solutions to the two-dimensional incompressible Euler equations in an infinite channel, whose far-field limits are uniformly non-stagnant shear flows. In the smooth category,for a broad class of prescribed far-field shear profiles, non-shear steady states exist via the construction of two-dimensional solutions of the...
For a finite associative unital ring $R$, the null ideal of $R$ is the collection of polynomials with coefficients from $R$ that send each element of $R$ to zero under evaluation. It was conjectured that the null ideal of $R$ is always a two-sided ideal of its overlying polynomial ring. The conjecture was proved to be false with the...
Epidemic models often pool air travel, commuting, and other mobility layers into a single weighted network. Pooling keeps the total imported infections into a region but discards the transport mode and route that delivered them, the information a mode-specific intervention needs. We make this precise for directed multilayer flows with...
We establish non-asymptotic Berry--Esseen bounds and bootstrap approximations for the Hilbert-space norm of nondegenerate $U$-statistics. Our triangular-array framework allows the kernel to take values in a separable Hilbert space $H_n$ that may vary with the sample size, thereby covering both infinite-dimensional spaces and Euclidean...
Paradigmatic interaction models explain how collective behaviors can emerge in complex systems from interactions among the constituent agents. In bio-inspired swarms, however, interactions alone may not suffice to bring the population to a desired aggregate configuration within a prescribed time horizon, as needed in applications...
The OBABO and BAOAB schemes and the other standard Strang splittings of kinetic (underdamped) Langevin dynamics are widely used Markov chain Monte Carlo algorithms. Under a suitable friction scaling, the underlying diffusion relaxes on a ballistic time scale, suggesting that these discretizations, suitably tuned, sample targets with...
We show that a Kähler surface with opposite Hermitian conformally Kähler structure defined by a foliation of complex curves is a QCH Kähler surface of Calabi type.
Suppose we are given an arbitrary line bundle $\mathcal{L}$ on a complex algebraic variety $X$, not necessarily smooth. For a positive integer $N$, suppose there exists a global section $s \in Γ(X, \mathcal{L}^{N})$ that defines an effective Cartier divisor $D$. If we denote $π: Y \rightarrow X$ to be the $N$-fold cyclic covering of...
$X$ is a Nakajima quiver variety. In this note we report the observation that the space parameterizing quasimaps from $\mathbb{P}^1$ to $X$, sending infinity to a given point, may be presented globally as the critical locus of an explicit function.
The Turing jump has no fixed point on the Turing degrees: $\mathbf a <_T \mathbf a'$ for every degree $\mathbf a$. After passing to the ideal completion, however, a natural fixed-point phenomenon appears. We study the Scott-continuous lifting $Γ:\operatorname{Idl}(\mathbf D_T)\to\operatorname{Idl}(\mathbf D_T)$, given by...
Spatial patterns, such as those in dryland vegetation models, have historically been studied in systems of reaction-diffusion systems with pattern onset via a Turing bifurcation from a spatially uniform state. More recently, spatial patterns have been considered in models that incorporate spatially extended interactions via nonlocal...
The embedding dimension of categorical predictors is usually selected through heuristic tuning, although it directly affects model complexity, approximation quality, and finite-sample generalization. This paper formulates embedding dimension selection as a constrained allocation problem. The main contribution is to show that embedding...
Many time series are not stable over their full observation horizon, but may contain scientifically meaningful periods during which a signal remains stable up to a prescribed tolerance. We formulate this as an existence test for stable intervals in a non-stationary regression model with dependent, locally stationary errors. For a...
Linear programming (LP) formulations offer a conceptually elegant approach to infinite-horizon, model-free nonlinear optimal control in continuous spaces. However, in addition to the curse of dimensionality, their practical use is limited by the difficulty of consistently obtaining bounded solutions. In this work, we use...
This paper describes the electricity markets and operational processes in the Irish power system and translates them into a Mixed Integer Linear Programming (MILP) model. The model is designed to estimate renewable generation Curtailment and Constraint. A full mathematical formulation is presented and tested on both a simple example...
For a hyper-Kähler fourfold $X$ of generalized Kummer type, we construct an infinitesimal deformation of the tangent bundle $T_X$ with non-zero Yoneda square. This is the first example of a stable hyperholomorphic bundle with obstructed deformations.
We present a quaternionic proof that the quadratic form $t^2+2x^2+5y^2+10z^2$ represents all positive integers, and that the form $t^2+x^2+7y^2+7z^2$ represents all natural numbers which are neither equal to $3 \cdot 7^\ell$ nor equal to $6 \cdot 7^\ell$, for any $\ell \in \mathbb{N}_0$. To do this we introduce a technique that may be...
We prove that the connected sum of a possibly noncompact area enlargeable manifold $M_1$ with an arbitrary spin manifold $M_2$ of the same dimension admits no complete Riemannian metric of uniformly positive scalar curvature. This extends a theorem of Wang--Zhang, where $M_1$ is assumed closed, to noncompact enlargeable summands; in...
We prove that the bracket width of the Lie algebra of vector fields on any smooth affine algebraic variety of dimension $n$ is at most $(n+1)^2$. We give improved bounds for some families of $\mathbb{C}^*$-varieties, in particular for $\mathrm{SL}_n(\mathbb{C})$ and for the Koras--Russell cubic threefold.
We study the fundamental problem of estimating the dependence structure of a centered stationary Gaussian process under local differential privacy (LDP). In this setting, the spectral density characterizes the dependence structure of the data and is the quantity to be estimated. Our main contribution is to close the open...
We show that the higher Legendrian homology of any Legendrian link given by the rainbow closure of a positive braid must necessarily vanish. The result is proven in the most general setting: for any number of strands and crossings, integrally and with one basepoint per component of the Legendrian link.
We study the long-time dynamics near Couette flow for the 2D Euler equations in unbounded geometries. We identify a mechanism of nonlinear inviscid damping at Yudovich regularity, distinct from classical phase mixing: velocity decay driven by spatial evacuation of vorticity. The mechanism leads to a geometry-sign classification of...
Two competitors choose starting vertices for independent, constant-speed random walks, and each site is acquired by its first visitor. We study the spatial geometry of the resulting first-passage location game. On every finite path the optimal strategies are exactly the distributions supported on the central vertices. The proof...