Mathematics

We define log conifold transitions for Fano threefold pairs of index two and study their deformation theory. Relying on the recent solution to the relative Clemens conjectures in this setting, we construct rational curves with normal bundle…

A factor of a graph is essentially a specific type spanning subgraph. In recent years, the spectral extremal problem of characterizing the existence of graph factors via eigenvalues has been widely studied. This paper focuses on fractional…

Tensor Train (TT) decomposition is a powerful technique for analyzing high-dimensional data. Existing algorithms for computing TT decompositions can be categorized into two main types: conventional batch-based approaches and recursive…

We study high-frequency semiparametric inference for ergodic regime-switching jump diffusions whose continuous coefficients are parametric and whose regime-wise L\'evy densities are unknown. The motivation is that jumps contaminate…

We prove that logarithmic capacity convergence for phase-union spectra of quasi-periodic Schr\"{o}dinger operators in the zero Lyapunov exponent regime is robust, requiring only continuity of the potential. Let $S^+(p/q)$ denote the union,…

In this paper, we investigate the effective resistance on the graph $G_N^{(r)}$, which is obtained by deleting all edges corresponding to circular distances $\{\pm1, \pm2, \dots, \pm r\}$ from the complete graph $K_N$. We utilize the cyclic…

We prove isoperimetric-type inequalities for pluriharmonic functions in the unit polydisc $\mathbb{U}^n$. Let $h^p(\mathbb{U}^n)$ and $b^p_{\mathbf{q}}(\mathbb{U}^n)$ denote, respectively, the pluriharmonic Hardy space and the pluriharmonic…

We establish the central limit theorem and the invariance principle for the inhomogeneous Diophantine approximations. The proof employs the cumulant method, which was developed by Bj\"orklund and Gorodnik to prove the central limit theorem…

The unitary-triangular (QR) factorization of linear algebra may be used to robustly and efficiently solve a linear system. Toward a comparable numerical method to solve a polynomial system of higher degree, this paper proposes an any-degree…

We establish Extreme Value Distributions for the closest encounter between trajectories generated by different maps defined in the same reference phase space. For a class of strongly mixing maps, we show that the limit distribution depends…

We derive several applications of the path-minimality theorem for adjacency $p$-energy proved in the companion paper. First, we prove the sharp inequality $$ \mathcal E_p^+(G)\ge \mathcal E_p^+(P_n), $$ where $P_n$ is the path on $n$…

This paper studies difference-of-convex (DC) optimization problems through smoothing descent techniques. In particular, we introduce the difference of high-order Moreau envelopes (HOME-DC) and establish its fundamental and differential…

We establish the generalized canonical bundle formula for generalized lc-trivial fibrations without the assumption on the nef part in the complex analytic setting. We also record the corresponding algebraic statement.

Let $\Omega$ be the superspace ring of regular differential forms on the affine space $\mathbb{C}^n$. If $G \subseteq GL_n(\mathbb{C})$ is a complex reflection group, the {\em $G$-superspace coinvariant ring} is the quotient $SR_G :=…

We establish local Gevrey regularity for the weak solution to parametric divergence-form diffusion elliptic PDEs, assuming the diffusion coefficient itself possesses local Gevrey parametric regularity over a non-compact domain. Here "local…

The Blaschke-Lebesgue theorem states that the Reuleaux triangle has the smallest area among planar convex bodies of a fixed constant width. We study how small bodies of constant width can be on the unit sphere $\mathbb S^n$ when $n$ is…

Lyapunov exponents are fundamental invariants in smooth ergodic theory describing the asymptotic infinitesimal behavior along typical orbits. This text aims to explain how and why to control Lyapunov exponents using entropy for smooth…

Generalized Fofana spaces were recently introduced as generalizations of Fofana spaces and Nakai's generalized Morrey spaces. In this paper, we establish the boundedness properties of the following operators in these spaces: fractional…

In this paper, we systematically investigate the structural and operator-theoretic properties of mappings contracting perimeters of triangles (MCPTs) within the generalized topological framework of complete $b$-metric spaces with…

We consider the space $C^1[0, 1]$ of continuously differentiable functions on the closed unit interval $[0, 1]$ and the space $\operatorname{Lip}[0, 1]$ of Lipschitz continuous functions on $[0, 1]$, equipped with the norms \begin{align*}…