arXiv preprints from January 1, 2026 through September 19, 2026 — 04:41:52 EST
In this paper, we present a high-order, stable summation-by-parts (SBP) finite difference method for solving the Vlasov-Maxwell system in a 2D2V phase space. Central SBP operators for the advection terms are not stable when the solution becomes non-smooth and fine-scale filamentary structures develop, as is typical in high-dimensional...
We complete the classification of compact simply connected homogeneous Einstein manifolds in dimension six by resolving the remaining cases for left-invariant Einstein metrics on $G=\mathrm{SU}(2)\times\mathrm{SU}(2)\cong S^3\times S^3$. Previous work leaves two cases for the isotropy group $K$, namely $K=\{e\}$ and $K\cong\mathbb...
This paper presents novel extremum seeking algorithms inspired by RMSProp dynamics and based on Lie bracket approximation techniques. To inherit the behavior of the classical continuous-time RMSProp algorithm, we introduce an extremum seeking scheme that exploits second-order Lie brackets, allowing the excitation of squared gradient...
Let $(M^n,g_0)$ be a closed smooth Riemannian manifold, with $n\geqslant 3$. We prove short--time existence and uniqueness for the "critical" {\em Ricci--Bourguignon flow} \begin{equation} \partial_t g=-2\operatorname{Ric}_g+\frac{R_g}{n-1}g\,. \end{equation} Up to a constant rescaling of time, this is the {\em Schouten flow}, since...
We prove a new estimate on Jacquet-Whittaker function for $\mathrm{GL}_n(\mathbb R)$, assuming that the Langlands parameters are purely imaginary and well-spaced. This gives an upper bound for the global sup-norm of the Whittaker function that matches the lower bound of Brumley-Templier in the exponent up to a linear error in $n$.
For classical knots, many characteristics are difficult to determine from arbitrary diagrams of the knot. Bridge number is of this type. It is possible to have a bridge presentation of a knot in which the number of bridges is only locally minimal, as shown by Ozawa and Takao. Here, we give a method for beginning with an arbitrary...
We introduce a nonlinear Poissonian fluctuating Boltzmann equation whose noise encodes both the fluctuations and the path large-deviation rate function of the underlying hard-sphere gas. Unlike the Gaussian-noise equations commonly studied in fluctuating hydrodynamics, the present equation raises a new difficulty: a Poisson random...
We develop a spread-based approach to finding induced cycles and apply it to two problems. First, we resolve the odd-hole gadget conjecture of Bradač, Draganić and Sudakov by constructing an $e^{O(k)}$-edge graph whose every $k$-edge-colouring contains a monochromatic induced odd cycle of length $O(\log k)$. As a consequence, for...
This paper studies the spectral properties and nonlinear asymptotic stability of a family of finite-time self-similar blow-up solutions to the three-dimensional Keller--Segel system constructed by matching interior and exterior profiles within the framework of matched asymptotic expansions. For every sufficiently large matching index...
Iima and Yoshino asked for an ideal $I$ in $S=k[x_1,x_2,\ldots]$, with $\operatorname{deg} x_i=i$, and a monomial order such that $S/I\cong k[x_i:i\equiv\pm1\pmod5], \operatorname{in}(I)=(x_i^2,x_ix_{i+1}:i\geq1).$ We construct such an ideal and monomial order over every field $k$ of characteristic different from $5$ containing an...
We consider a system of $N$ interacting bosons in a rotating harmonic trap in $\mathbb{R}^2$, where the two-body interaction is attractive and scaled as $N^{2α}U(N^αx)$ with $0<α<1/12$, and the three-body interaction is repulsive and scaled as $N^{4β}W(N^βx,N^βy)$ with $0<β<1/24$. In the mean-field limit, the ground state energy is...
We prove that a nonconstant polynomial $f\in\mathbb{C}[x_1,x_2,x_3]$ is cylindrical (that is, $f\in\mathbb{C}[x_1,x_2]$ after an invertible linear change of coordinates) if and only if its bordered Hessian determinant vanishes identically. The same conclusion holds over $\mathbb{R}$. We also give explicit counterexamples to this...
We study slice regular functions on the real division algebras $\mathbb{H}$ and $\mathbb{O}$ from the point of view of equivalence under automorphism and conjugation actions. Motivated by recent orbit-theoretic descriptions in terms of the invariants $(Tr,N,cdiv)$, and by the quaternionic theory of $*$-conjugation by semiregular...
Let \(β(G)\) denote the minimum size of a feedback edge set of a digraph \(G\), and let \(γ(G)\) denote the number of unordered pairs of nonadjacent vertices. Motivated by the Chudnovsky--Seymour--Sullivan conjecture for \(3\)-free digraphs, we study the corresponding feedback-edge problem for bipartite digraphs. In the bipartite...
Let $R_n$ be the infimum of the inradii of $\{z:|p(z)|<1\}$ over monic degree-$n$ polynomials whose zeros lie in the closed unit disk. We prove $nR_n\toπ/2$, matching the asymptotic obstruction supplied by $z^n-1$. We first establish the exact universal radius $2^{1/n}-1$ for disks centered at zeros, which recovers the $(\log2)/n$...
We prove that the Dirichlet $p$-torsion function $u_p$ converges to the distance to the boundary $d$ at the rate $O(1/p)$ in the uniform norm, on every bounded domain and with a constant depending only on the dimension and the diameter. The upper bound comes from a radial barrier with its pole at a boundary point, which is an...
A complete one-ended three-manifold with strictly positive Ricci curvature is constructed such that $$ \limsup_{R\to\infty}\frac1R\int_{B(p,R)} Scal\,dV=+\infty. $$ The construction combines an explicit toric lens carrying a large scalar-curvature integral with a three-dimensional angular pair of pants and an adaptive sequence of...
The Donoho--Stark uncertainty principle asserts $N^d\le|E|\,|Σ|$, and the additive energy uncertainty principle of Aldahleh--Iosevich--Iosevich--Jaimangal--Mayeli--Pack refines it to $1\le|E|\cdot\|1_Σ\|_{U^2}^{4/3}$. It has been conjectured that the natural higher-order analogue \[ 1\le |E|\cdot\|1_Σ\|_{U^k}^{2^k/(k+1)} \] holds for...
We prove the conjecture of Bergsma and Dassios that their sign covariance $τ^{*}$ is nonnegative for every bivariate law and vanishes exactly under independence. Previous results covered discrete and absolutely continuous laws, their mixtures, and laws with atomless margins. We construct tie-symmetrised extensions $\widetilde D$ and...
We prove a uniform shifted anticoncentration theorem for the hafnian of a real Gaussian Gram matrix under an explicit condition on the row dimension. After normalization by its root mean square, the law has a bounded continuous density, maximal at zero, and every interval has probability bounded by an explicit coefficient times its...
We study nonuniform sampling for positive operator systems. Given a locally finite set \(T\subset[0,\infty)\), we determine when exact observability of \(\{CA^n\}_{n\in\mathbb N}\) implies exact observability of \(\{CA^t\}_{t\in T}\) for every positive operator \(A\) and every observation operator \(C\). Using the Stein identity and a...
A criterion for the convexity of a two-dimensional domain is proved in terms of the solution of a boundary value problem for the modified Helmholtz equation.
Let $X$ be a $(q-1)$-connected rational space of finite type, where $q\ge2$, with homotopical nilpotency $nil_h(X)=n\ge1$. If $H^{>N}(X;Q)=0$ and $N\le q(n+3)-3$, we prove that $Hnil(X)=n$. More precisely, the sufficient bound is $N\le a_n(M_X)+2q-3$, where $a_n(M_X)$ is the first nonzero internal cohomology degree of $(M_X^+)^{n+1}$...
In Finite groups with a small number of cyclic subgroups. Czechoslovak Mathematical Journal 75.3 (2025): 839-851. The authors classified all the groups having 13 cyclic subgroups. In this paper, we give a new proof for the classification of all finite groups having exactly 13 cyclic subgroups.
Various persistent invariants have been developed in recent years. In this paper, we develop a method based on homological algebra for deriving central limit theorems for persistent Betti numbers associated with $\mathbb{R}$-indexed chain complexes constructed from a homogeneous Poisson point process of unit intensity on...