Mathematics

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}\,…

This paper establishes Bismut-type formulas and gradient estimates for Feynman--Kac semigroups on Riemannian manifolds with boundary, under geometric conditions formulated in terms of Ricci curvature $\mathrm{Ric}_Z \geq K$ and second…

Partial cubes are a fundamental class of graphs that admit isometric embeddings into hypercubes. Klav\v{z}ar and Kov\v{s}e [Ars Combin. 93 (2009), 77--86] observed that the opposite semicubes of every harmonic-even partial cube are pairwise…

Phase unwrapping is an essential preprocessing step for phase-based MRI applications, including susceptibility mapping, field mapping, thermometry, and MR elastography. We present Iterative Laplace-Based Phase Unwrapping (ILPU), a bi-level…

In their recent paper, Bergfalk and Smythe prove that the isometry equivalence relation on hyperbolic surfaces with finitely-generated fundamental group is concretely classifiable, and ask whether the same result holds true for…

We develop a discrete-time renewal framework in which renewal events evolve along multiple time coordinates and the sojourn mechanism is described by a general distribution on the multi-index lattice. The resulting processes, called…

We study arrangements of smooth conics and lines in the complex projective plane whose singularities are limited to nodes, tacnodes, and ordinary triple points. The first part of the paper gives numerical restrictions for plus-one generated…