Research
Research
Research
Research
32,525+ open-access research outputs.
In 1967 Hajnal and Juh{\'a}sz showed that the cardinality of a first-countable Hausdorff space with the countable chain condition has cardinality at most $\mathfrak{c}$, the cardinality of the real li…
Building on the genus-3 reduction $C_A : w^2 = \lambda^8 + A \lambda^4 + 1$ established in our companion paper (arXiv:2604.09328), we give an unconditional proof of the perfect-cuboid conjecture ("Con…
The impossibility of eliminating hallucination, understood here as incorrect definite answers, in sufficiently expressive yes-or-no formal domains is an immediate consequence of classical undecidabili…
This work investigates minimal parametric networks in hyperspaces of closed subsets of metric spaces endowed with the Hausdorff distance. It is shown that the problems of finding such networks are non…
We consider a class of nonlinear parabolic equations \[ \dfrac{\partial}{\partial t} b(u)-\nabla \cdot (A(x,t,u,\nabla u))+H(x,t,\nabla u)=f , \] where $H$ is a nonlinear lower order term sati…
A skew Bollob\'{a}s system $\mathcal{P}=\{(A_i,B_i):1\leq i\leq m\}$ is a collection of pairs of disjoint subsets of $[n]$ such that $A_i\cap B_j\ne\emptyset$ for any $1\leq i<j\leq m$. Denote by $S_1…
Let $G = \mathrm{SL}(n,\mathbb{C})$, let $B$ be a fixed Borel subgroup, and let $P \supset B$ be a parabolic subgroup determined by a composition $(c_1,\dots,c_k)$ of $n$. Write $P'$ for the derived g…
We prove a Positivstellensatz for operator-valued noncommutative polynomials that are positive on matrix convex sets. Specifically, let $p$ be an operator-valued polynomial in $B(H)\otimes C<x>$ of de…
Many well-known theorems establish sufficient criteria for linearizability of a vector field in terms of the eigenvalues of its linear approximation. By attaching weights to coordinates so that some d…
We study groups endowed with Alexandroff topologies and show that no non-discrete Alexandroff topology can turn a group into a topological group. This settles negatively the basic existence problem fo…
Coisotropic A-branes were introduced by Kapustin--Orlov to enlarge the Fukaya category of a symplectic manifold in a way that aligns with predictions from homological mirror symmetry. From a mathemati…
We define the notion of couple density $(D, \mathbf b)$ where $D$ is a non-empty subset of $\mathbb Z^{m}$ and $ \mathbf b$ a fixed element in $\{0, \cdots, q-2\}^{m};$ We determine a minimum in terms…
This paper explores the restriction behavior of silting-induced $t$-structures and co-$t$-structures on triangulated categories endowed with metrics. For compactly generated triangulated categories ad…
Based on discrete observations, we develop a test to infer if the volatility function $\sigma(\cdot)$ within the nonparametric Gaussian white noise model $dY_t = \sigma(t)dW_t$ is constant. The testin…
Let $q=p^n$, $r\in \mathbb{Z}_{\ge 2}$, $e=q-1$, and $k=\frac{q^r-1}{e}$. In this paper, we study the cyclotomic numbers $(a,b)_{q-1}$ over $\mathbb{F}_{q^r}$. We prove that $(a,b)_{q-1}\le \left\lcei…
We prove the congruence $\sum_{1 \leq k < \sqrt{N}} \sigma_0 (N - k^2) \equiv 0 \pmod 4$, where $\sigma_0(m)$ denotes the number of positive divisors of $m$, for $N = An + B$ with $(A,B) \in \{ (16,14…
In the previous paper, the author showed that for a smooth family $X \to \mathbb{X} \to B$ of a homotopy $K3$ surface, the obstruction for the tangent bundle along the fibers $T_B \mathbb{X}$ to have …
We consider the two families of even polynomials $\Xi_n$ and $\Lambda_n$ studied in~\cite{TallaWaffo2026arxiv2602.16761}, together with the rescaled polynomials $\widetilde{\Xi}_n(x):=\Xi_n(\sqrt{x})$…
We give a metaplectic proof of Hilbert reciprocity, and hence of quadratic reciprocity, in which the local phase is the Kashiwara--Maslov phase of a triple of Lagrangians. In rank two the phase of the…
Motivated by branching problems for principal series representations of the Lie group $G = GL(n,\mathbb R)$, we consider all pairs $(G', P)$ with $G'$ being the Levy factor of a parabolic subgroup of …
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