数学

This work presents the analysis and numerical simulation of a stationary drift-diffusion model for electrical discharge in micro-electro-mechanical systems (MEMS). The model couples Poisson's equation for the electrostatic potential with…

We establish weighted Gaussian approximations for the uniform empirical and quantile processes and for their increments ending at a fixed point \(t\in(0,1)\). We first place the classical weighted approximations for the ordinary processes…

We study the coupon collector's problem in a generalized setting where each draw reveals a fixed number of coupons and the sampling mechanism is required to be \emph{fair}, meaning that every coupon appears with the same frequency among the…

Let $(T_1,\ldots,T_d)$ be a commuting $d$-tuple of Ritt$_E$ operators on some UMD Banach space $X$. We show that $(T_1,\ldots,T_d)$ admits a bounded $H^\infty$-functional calculus if and only if $T_k$ is an $R$-Ritt$_E$ operator for every…

We prove that convexity of the Boltzmann entropy at Wasserstein barycenters is strong enough to distinguish Hilbert spaces from general Banach spaces. Thus Wasserstein barycenters provide an intrinsic optimal-transport test for Hilbertian…

We investigate a variational problem for eigenvalues of the Laplace-Beltrami operator on smooth manifolds with respect to Radon measures belonging to a suitable class; we are motivated by conformal eigenvalues in dimension two. Our main…

For minimizers of a degenerate diffusion functional with a singular reaction term, we prove that the free boundary is $(n-1)$-rectifiable. The argument relies on a suitable integrability property, derived from a pointwise gradient estimate,…

Construction of Earth-Moon transfers is the basis of missions to explore the Moon and cislunar space. The traditional grid search method suffers from a relatively low convergence rate and computational efficiency, mainly focusing on the…

We classify, up to conjugacy, the 3-dimensional subalgebras of the Lie algebras associated with the 4-dimensional Thurston geometries whose isometry groups have dimension 4. Since homogeneous hypersurfaces arise as orbits of subgroups of…

We investigate the existence of segregated rotating waves, arising in the singular limit of competition-diffusion systems of the type \[ \partial_t u_i -\partial_{xx} u_i = f(u_i)-\beta u_i \sum_{j \neq i} a_{ij} u_j,\qquad…

A graph $G$ is $\tau_k$-maximal if $G$ contains no subgraph admitting $k+1$ edge-disjoint spanning trees, while the addition of any edge in the complement of $G$ yields a subgraph that admits $k+1$ edge-disjoint spanning trees. In this…

We present a fast, high-order algorithm for the free-space fractional Fokker-Planck equation (FFPE) in arbitrary spatial dimension. Its fundamental solution, corresponding to a Dirac-delta initial condition, is obtained from the explicit…

Classical works of Hall and McLain show that solubility and local nilpotency play a key role in deriving finite generation in groups from maximal or minimal conditions on normal subgroups. In this work, brace-theoretical analogues of Hall's…

We identify necessary and sufficient conditions for a class of random mappings to send exchangeable $\{0,1\}$-sequences to other exchangeable $\{0,1\}$-sequences. We call this property the propagation of exchangeability, and show that any…

The largest matching root $\mu(G)$ of a graph $G$ is that of its matching polynomial. In this paper, all limit points of the largest matching roots of graphs are determined. More precisely, we identify the limit points of the largest…

We prove that there exists a finite unit-distance graph in the plane with independence ratio strictly smaller than 1/4, answering a question of Erd\H{o}s. Our proof closely follows the framework of Matolcsi, Ruzsa, Varga, and Zs\'amboki,…

We prove that for any matrix $A \in \mathbb{R}^{m \times n}$ and any $\varepsilon \in (0, 1/2]$ there is a diagonal matrix $D \in \mathbb{R}_{\geq 0}^{m \times m}$ with at most $O(\frac{n}{\varepsilon^2} \log(\frac{1}{\varepsilon}))$…

We prove global-in-time strong pathwise well-posedness for a stochastic fluid-structure interaction problem coupling a two-dimensional incompressible Navier-Stokes fluid to a one-dimensional damped Kirchhoff plate. The coupling is imposed…

We study a class of nonconvex cardinality-constrained optimization problems arising in sparse learning. These problems are NP-hard due to the combinatorial nature of sparsity constraints. We introduce a Reservoir Zero-Coordinatewise…

The signless Laplacian matrix of a graph $G$ is $Q(G)=D(G)+A(G)$, where $D(G)$ and $A(G)$ are the diagonal degree matrix and the adjacency matrix of $G$, respectively. The signless Laplacian spectral radius of $G$ is the largest eigenvalue…