数学

We study oriented surfaces in the Heisenberg space $\mathrm{Nil}_3$ whose mean curvature $H$ at each point is $H=\langle N,\partial_z\rangle+\lambda$, where $N$ is the unit normal, $\partial_z$ is the vertical Killing vector field and…

Ziegler proved that every simplicial $d$-dimensional $0/1$-polytope has at most $2d$ vertices, and asked whether equality forces the polytope to be centrally symmetric and hence, equivalently, a $0/1$-realization of the $d$-dimensional…

In this article, we investigate V-line transforms for symmetric $m$-tensor fields whose support lies inside a disk of radius $R$ and centered at the origin. We provide an explicit characterization of the kernel of the V-line transforms…

A $\lambda$-translator in $\mathbb{S}^2\times\mathbb{R}$ is an oriented surface whose mean curvature $H$ satisfies $H=\langle N,\partial_z\rangle+\lambda$, where $N$ is the unit normal, $\partial_z$ is the vertical Killing vector field…

We study the minimality of the system of root functions associated with a Sturm--Liouville problem whose boundary condition depends linearly on the eigenparameter. Two different criteria for minimality were previously obtained using…

We consider the calibration of probability forecasts. Several notions of calibration exist when the forecaster issues a single forecast for each of the observations that is to be predicted. We extend one of these notions, auto-calibration,…

In this paper, we establish a comparison principle for non-negative weak solutions to a class of doubly nonlinear parabolic fractional partial differential equations within a space-time cylinder…

Let \[ \rho(q)=\sum_{m\geq 0}\frac{q^{2m(m+1)}}{(1+q+q^2)(1+q^3+q^6)\cdots(1+q^{2m+1}+q^{4m+2})} =\sum_{n\geq 0}r(n)q^n \] be Ramanujan's third order mock theta function. We prove the sign law \[ r(3m)>0,\qquad r(3m+1)\leq 0,\qquad…

Conformal prediction and its variants, including the split conformal prediction, provide a distribution-free framework for uncertainty quantification by constructing prediction intervals or sets with finite-sample coverage guarantees. The…

We consider a family of continuous-time Markov chains with finite strongly connected transition graph and rates $\left(r_N\right)_{N>0}$ depending on a parameter $N$, so that, when $N$ is large, transitions may happen on different time…

Classical minimax lower bounds for testing are typically derived for fixed error probabilities, while high-confidence results often impose a common failure probability. We study prescribed-error testing, in which the level and the target…

We study the symmetrical Dziobek configurations where, in $\mathbb{R}^{d}$, there are $d$ bodies with unit masses at the vertices of a regular $(d-1)$-dimensional simplex of unit edge length and two more bodies with nonzero masses $s,k$ are…

The feedback arc set problem on tournaments arises in a rich variety of applications, and has been studied extensively in several research fields over the past six decades. It is well known that this problem is $NP$-hard and admits a…

This paper investigates the long-times behavior of the Fisher-KPP equation with slowly decaying initial data in an almost periodic medium. We mainly focus on two classes of initial data: exponentially decaying initial data and inital data…

The Kaplansky radical of a field consists of the nonzero elements represented by every norm quadratic form in two variables. D.~Kijima and M.~Nishi conjectured that, for quadratic extensions, the Kaplansky radicals are related by the norm…

A real quadratic field satisfies Hammarhjelm's condition if its ring of integers has unique factorization, and the Minkowski lattice of its ring of integers contains no point in a certain rectangle determined by the fundamental unit. Such…

In this paper, we prove estimates for the Stokes resolvent problem with no-slip boundary conditions on the half space in weighted $L^p$-spaces. The weights we consider are power weights both inside and outside the Muckenhoupt range. Our…

This paper studies free stochastic differential equations driven by free Brownian motion. Under local operator Lipschitz and Lyapunov-type conditions on the coefficients, we prove the global well-posedness of solutions in the noncommutative…

We report the exact value of the number of labeled partially ordered sets (equivalently, labeled $T_0$ topologies) on 19 points, P(19) = 646099441937791106493755218560442089979, a 39-digit integer extending OEIS A001035, whose largest…

In this paper, we study distribution-dependent stochastic differential equations on the domain $\mathcal O=\mathbb T^d$ or $\mathbb R^d$, $d\geq 2$, of the form \begin{align*} {\rm d}X_t = v(t,X_t,\rho_t)\,{\rm d}t + \sqrt{2}\,…