arXiv preprints from January 1, 2026 through July 20, 2026 — 18:25:16 EST
We study conjugate-type phenomena for complex-valued harmonic quasiregular mappings in the unit disk across three function space families: $Q(n,p,α)$, $F(p,q,s)$, and the non-derivative $M(p,q,s)$. For a harmonic $K$-quasiregular mapping $f=u+iv$, we first show that if the real part $u$ belongs to $Q_h(1,p,α)$ (with $α>-1$ and...
The double-exponential Sinc-collocation method is known as a super-accurate method for solving initial value problems of ordinary differential equations, for which the error decreases almost exponentially as a function of the number of sample points in the temporal direction, $N$. However, this method requires solving nonlinear...
How many $n$-step polygons exist that contain a given vertex of an infinite quasi-transitive graph $G$? The exponential growth rate of such polygons is identified as the connective constant when $G$ has sub-exponential growth and possesses a so-called square graph height function. The last condition amounts to the requirement that $G$...
In this paper, we mainly study the Castelnuovo-Mumford regularity of the generalized binomial edge ideals of graphs. We show that this number can be any integer number from $2$ to $n-1$ where $n$ is the number of vertices in the underlying graph. We are able to show this, after giving some tight lower and upper bounds for the...
A theorem of Meyer and Reisner characterizes ellipsoids by the collinearity of centroids of parallel sections: if $Ω\subset\mathbb{R}^{n+1}$ is a convex body such that for every $n$-dimensional subspace $M\subset\mathbb{R}^{n+1}$ the centroids of the sections $(x+M)\cap Ω$ are collinear, then $Ω$ is an ellipsoid. We study natural...
This paper studies phase and norm retrieval by subspaces. We first investigate norm retrieval by hyperplanes. We show that if $N$ hyperplanes $\{\varphi_i^\perp\}_{i=1}^N\subset \mathbb{R}^N$ allow norm retrieval and the vectors $\{\varphi_i\}_{i=1}^N$ are linearly independent, then these vectors must be an orthonormal basis for...
We discuss the low energy resolvent estimates for the Schrödinger operator with slowly decaying attractive potential. The main results are Rellich's theorem, the limiting absorption principle and Sommerfeld's uniqueness theorem. For the proofs we employ an elementary commutator method due to Ito--Skibsted, for which neither of...
In this paper, we study normalized solutions for the following critical Schrödinger-Bopp-Podolsky system: $$-Δu + q(x)φu = λu + |u|^{p-2}u + \bigl(I_α* |u|^{3+α}\bigr)|u|^{1+α}u,\quad \text{in } Ω_r,$$ $$-Δφ+ Δ^2φ= q(x)u^2, \ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\ \text{ in } Ω_r,$$ where $Ω_r \subset \mathbb R^3$ is a smooth...
We consider inverse eigenvalue problems for the perturbed Bessel operator in $L^{2}(0,1)$. (1) For the case where the angular-momentum quantum number $\ell\in\mathbb{N}\cup\{0\}$, we establish a uniqueness result for the inverse spectral problem by utilizing the closedness condition of a certain function system constructed based on...
It is shown that Pythagorean triples can be used to generate matrices that have integer eigenvalues for all permutations of their coefficients, via simple formulas. For example, each and every permutation of the $2\times2$ matrix coefficients $\{12,6,7,1\}$, generated by the Pythagorean triple $(5,12,13)$, yields a matrix with integer...
We present SaddleScape V1.0, a Python software package designed for the exploration and construction of solution landscapes in complex systems. The package implements the High-index Saddle Dynamics (HiSD) framework and its variants, including the Generalized HiSD for non-gradient systems and the Accelerated HiSD. SaddleScape V1.0...
Problem 20.21 of Mazurov and Khukhro (Unsolved Problems in Group Theory: The Kourovka Notebook, 20th Issue, 2022), contributed by M.~Conder and attributed to G.~Verret, asks whether there exists a finite group $G$ with two normal subgroups $K$ and $L$ of index $12$ such that $K \cong L$, but with non-isomorphic quotients $G/K \cong...
High-dimensional integration with respect to complex target measures remains a fundamental challenge in computational science. While Flow Matching (FM) offers a powerful paradigm for constructing continuous-time transport maps, its deployment in high-precision integration is severely limited by the discretization bias inherent to...
This paper investigates the wall structure of the space of stability conditions on Hirzebruch surfaces. Using the gluing construction of \cite{CP} and \cite{Uch} with respect to a fixed semiorthogonal decomposition, we focus on two main objectives: observing the intersection of the geometric chamber $U(S) \subset \mathrm{Stab}(Σ_e)$...
Given a compact cube complex $X$ that splits as a graph of virtually special cube complexes. Suppose that the fundamental groups of edge spaces are cyclonormal in the fundamental groups of adjacent vertex spaces. We show that $π_1X$ has finite stature with respect to vertex groups in the sense of Huang-Wise. In particular, when vertex...
We study the expectation-maximization (EM) algorithm for general latent-variable models under (i) distributional misspecification and (ii) nonidentifiability induced by a group action. We formulate EM on the quotient parameter space and measure error using an arbitrary integral probability metric (IPM). Our main results give (a) a...
The aim of this article is to use Banach lattice techniques to study coordinate systems in function spaces. We begin by proving that the greedy algorithm of a basis is order convergent if and only if a certain maximal inequality is satisfied. We then show that absolute frames need not admit a reconstruction algorithm with respect to...
Let $μ$ be a probability measure on $\mathbb C$, and let $P_n$ be the random polynomial whose zeros are sampled independently from $μ$. We study the asymptotic distribution of zeros of high-order derivatives of $P_n$. We show that, for large classes of measures $μ$, the empirical distribution of zeros of the $k$-th derivative...
In 1987 Hiroshi Maehara conjectured that a graph can be represented by vectors considered adjacent when not orthogonal (a faithful orthogonal representation) in codimension the minimum degree of the graph. Without settling the conjecture, Làslò Lovàsz, Michael Saks, and Alexander Schrijver (LSS) showed that a codimension of vertex...
We prove that continuous spectrum- and commutativity-preserving maps to $\mathcal{M}_n(\mathbb{C})$ from the space of normal (real or complex) $n\times n$, $n\ge 3$ matrices with spectra contained in a given continuous-injection interval image $Λ\subseteq \mathbb{C}$ or $\mathbb{R}$ are (a) conjugations; (b) transpose conjugations, or...
We show that for the standard sinusoidal Winfree model, a coupling strength exceeding twice the maximal magnitude of the intrinsic frequencies guarantees the convergence of the system for Lebesgue almost every initial data. This is proven by first showing, via an order parameter bootstrapping argument, that the pathwise critical...
We consider Cesáro operator on the Hardy space $H^p(\mathbb{C}_+)$ in the upper half-plane for $1<p<\infty$. In \cite{AS} it was proved that for all $1<p<\infty$ the spectrum of the operator $V=\frac{2(p-1)}{p}C-I$ is located on the unit circle and in \cite{ABC1} the authors of this note showed that for $p=2$ operator $V$ is unitary....
In this paper, for $1 \leq p, r < \infty$ we characterize those symbols $f$ so that the induced Hankel operators $H_f$ are $r$-summing from Fock spaces $F^p_α$ to $L^p_α$. The main result shows that the $r$-summing norm of $H_f$ is equivalent to the $\mathrm{IDA}^{κ, p}$-norm of $f$, where $κ$ is a positive number determined by $p$...
The adjacency-diametrical matrix (AD matrix) of a connected graph $G$ with diameter $d$, denoted by $AD(G)$, is the matrix indexed by the vertices of $G$ in which the $(i,j)$-entry of $AD(G)$ is $1$ if $d_G(v_i,v_j)=1$, is $d$ if $d_G(v_i,v_j)=d$, and $0$ otherwise, where $d_G(v_i,v_j)$ denotes the distance between the vertices $v_i$...
We consider a system of $N$ Hawkes processes and observe the actions of a subpopulation of size $K \le N$ up to time $t$, where $K$ is large. The influence relationships between each pair of individuals are modeled by i.i.d.Bernoulli($p$) random variables, where $p \in [0,1]$ is an unknown parameter. Each individual acts at a {\it...