数学

We study fundamental gaps for the Dirichlet \(p\)-Laplacian on bounded convex domains with convex potentials. We prove log-concavity of the positive first eigenfunction by a regularization and two-point maximum principle. For \(N\geq2\), we…

We perform a linearized stability analysis of the Vlasov--Fokker--Planck equation obtained as the mean-field description of a stochastic spontaneous aggregation model with memory. Memory is represented by a chain of $K$ internal variables.…

The less-than-truckload (LTL) industry plays a vital role in enhancing the efficiency and sustainability of logistics systems, as LTL shipments offer greater consolidation opportunities than full-truckload shipments. Despite of this…

We introduce synthetic buildings for each finite group $G$ and prime $p$. These are $G$-simplicial complexes, among which are the $p$-subgroups complex of K.S. Brown, and also the buildings of finite groups of Lie type in characteristic…

We study the stochastic resistive Hall--magnetohydrodynamic (Hall--MHD) system on bounded convex polyhedral domains, subject to nonlinear perfectly conducting boundary conditions. The system is driven by multiplicative Gaussian forcing in…

We give the minimum of category theory necessary for understanding the definition and applications of Grothendieck topos. We state the basic properties of sites and sheaves, and give applications to the theory of moduli. We prove that for…

Following ideas of Kapustka-Kapustka, we use Lagrangian fibrations to construct twisted hyperholomorphic sheaves on products of hyperk\"ahler manifolds of K3$^{[n]}$- and OG10-type. As applications, we prove the Lefschetz standard…

We prove the conjecture of Donnelly et al. that a certain class of Littlewood-Richardson tableaux are equinumerous with peakless Motzkin paths of length $n$. Furthermore, we construct an explicit bijection between this class of tableaux and…

Recently we started building a bridge between two cases of Langlands duality. The latter is one of the most influential topics in mathematical research. It has many different appearances and influential subtopics. Yet there is a topic that…

We prove that every Kreiss bounded $C_0$-semigroup $(T_t)_{t\geq0}$ on a Hilbert space satisfies \[ \|T_t\|\leq C(1+t)^{1-\varepsilon_K}, \qquad t\geq0, \] where $\varepsilon_K>0$ depends explicitly only on the Kreiss constant. This…

We develop an intrinsic theory of weighted, inhomogeneous Besov spaces on general homogeneous Lie groups without recourse to group-specific arguments. Starting from a definition in terms of localised test functions, we establish an…

We classify universal divisor-profile separation for coprime polynomial pairs of arbitrary degree and for all pairs of degree at most two. For \(A\subset\N\) and \(m\in\Z\), let \(d_A(m)\) count the members of \(A\) dividing \(m\). For…

A well-known conjecture in complex geometry states that a compact Hermitian manifold with constant Chern holomorphic sectional curvature must be K\"ahler when the constant is nonzero and Chern flat when the constant is zero. The conjecture…

In this article we consider bridging between two mixture probability measures. In particular, given access to a Markov kernel between two component distributions, we provide a general mechanism to generate samples from one mixture to the…

For each nonnegative integer $m$, we construct smooth symmetric $3\times 3$ coefficient matrices $A_m$ satisfying the fixed ellipticity bound \[ I\leq A_m\leq 2^{81}I \] for which the smooth solutions of uniformly elliptic equations in…

We construct a simple $\lambda$-double Lie algebra on $k[t,t^{-1}]$ for every nonzero $\lambda\in k$. We then show that the analogous two-sided construction of weight zero is also simple. Both products admit natural coefficient realizations…

We study two-weight weak-type estimates for the operator $S_v f = \mathcal{T}(fv)/v$, where $\mathcal{T}$ is the Hardy-Littlewood maximal operator or a Calder\'on-Zygmund operator (CZO) and $v$ is a weight. Concretely, under certain…

In this note, we construct moduli spaces of super-representations of quivers by extending King's Geometric Invariant Theory (GIT) framework to the super setting. Using the even part of super general linear groups and a parity-shifting…

We prove new comparison results between the Wasserstein distance and its sliced and max-sliced counterparts. First, we show that the H\"older exponent~$\frac{2}{d+2}$ obtained by Bobkov and G\"otze for the max-sliced 1-Wasserstein distance…

The Dynamic Mode Decomposition (DMD) has been consolidated as a basic tool for data-driven analysis of dynamical systems, allowing simultaneous identification of coherent structures and their dynamics from time-resolved measurements.…