数学

In 1973, Russian mathematician I.R. Shafarevitch delivered a lecture to the G\"ottingen Academy of Sciences on the purpose of mathematics. The conclusion he reached in his address is that the ultimate purpose of mathematics must be…

The ranking of fuzzy numbers has become a challenging task in fuzzy set theory due to their complex, multi-dimensional nature. While the Klir-Yuan partial order provides a natural term-wise comparison of $\alpha$-cuts, it often leaves many…

This paper treats variable-order time-fractional subdiffusion with discontinuous coefficients across a curved interface using $L2\!-\!1_\sigma$ time stepping on graded meshes and a symmetric interior penalty FEM on body-fitted meshes.…

Let $(X,\mu)$ be a measure space and let $1< p< \infty$. We study quantitative stability refinements of Minkowski's inequality \[ \| f + g\|_{p}\leq \| f\|_{p} + \| g\|_{p} \] for real-valued functions in \(L^p(X,\mu)\). We first establish…

Anytime-valid confidence sequences and e-processes are built almost universally from one recipe: average exponential test statistics over a prior on the tilting scale, then invoke Ville's inequality on the resulting nonnegative…

This article relates the theory of embedded contact homology (ECH) with the dynamics of Anosov flows. We show that in many cases the ECH capacities of a symplectic 4-manifold are infinite, including cotangent disk bundles over closed…

We analyze Bregman ADMM for nonconvex linearly constrained problems under two-sided relative smoothness, a condition that replaces the standard Lipschitz gradient assumption with a Hessian comparison relative to a Bregman kernel. This…

In recent work the authors determine complete columns of symmetric-group decomposition matrices in odd prime characteristic $p$ labeled by $p$-regular partitions for which every hook of length divisible by $p$ has even arm length. In the…

This paper introduces a new application of the perfectly matched layer (PML) for mitigating model top wave reflections in geophysical fluid models. Typically, a strong Laplacian or Rayleigh damping sponge layer is used near the upper…

We introduce Carleson analogs of the Bourgain--Brezis--Mironescu spaces $B$ and $B_0$ by measuring mean oscillation over upper Carleson tents. For these spaces, denoted by $B_{\mathcal C}^p$ and $B_{\mathcal C,0}^p$, we prove two types of…

We consider the initial value problem (IVP) for a two-parameter family of derivative nonlinear Schr\"odinger equations on the torus, known as the Majda-McLaughlin-Tabak (MMT) model arising in weak wave turbulence theory. For positive…

We study commutative topological algebras naturally associated with translation-invariant reproducing kernel Hilbert spaces whose direct integral decomposition has one-dimensional fibers. Starting from the bounded algebra of…

We construct a family of continua and pointwise periodic homeomorphisms realizing arbitrary polynomial entropy values in $[0,+\infty]$. In particular, this provides examples of pointwise periodic homeomorphisms with positive polynomial…

We study the optimal complexity of first-order methods under the $\alpha$-Polyak-Lojasiewicz condition with $\alpha\in[1,2)$. This condition bounds the suboptimality gap by a power $\alpha$ of the gradient norm; $\alpha=2$ recovers the…

This article presents a unified overview of contact Hamiltonian geometry as a natural framework for the description of dissipative and non-conservative systems. Starting from the symplectic cover of a contact manifold, we clarify the…

This paper continues the study of resonance phenomena initiated in [3] for rank-one perturbations. We consider finite-rank multi-parameter perturbations $H_\alpha$ of the Laplacian on \(L^2(\mathbb{R}^3)\) and establish Breit--Wigner-type…

Recent progress on the structure of the quantum connection for monotone symplectic manifolds has used two approaches, which share the common feature of reducing to mod $p$ coefficients. We refine and compare those approaches. In particular,…

This paper studies the mean field game of mutual holding proposed by Djete and Touzi(AAP, 2024), and consider the case where the interactions among agents are described by a graphon. We adopt the formulation on the enlarged space which is…

We consider the semilinear parabolic equation \[ \partial_t u = \Delta u + 2\mathfrak{q}\,\delta_{\mathbb{S}}\,\nabla u + |u|^{p-1}u \qquad \text{in } (0,\infty)\times\mathbb{R}^N, \] where $|\mathfrak{q}|\le 1$, $p>1$, and $\mathbb{S}$ is…

We consider solutions of uniformly elliptic equations with measurable coefficients. We assume that the lowest eigenvalue of the coefficient matrix is at least $K^{-1}$ and the largest eigenvalue is at most $K$. In three and higher…