Research
Research
Research
Research
10,663+ open-access research outputs.
We show that under $\mathsf{ZF} + \mathsf{CC}_{\mathbb R}$, if the Ramsey property holds for all sets in a good pointclass $\Gamma$, then there is no MAD family in $\Gamma$, proving a long-standing co…
In this paper, we prove several rigidity results for complete noncompact manifolds with nonnegative intermediate curvatures. We show that when either $3\leq n\leq 5$, $1\leq m\leq n-1$, or $6\leq n\le…
Alternating sign matrices (ASMs) arise as the Dedekind-MacNeille completion of the Bruhat order on the symmetric group. They enjoy fruitful combinatorial and geometric properties, with a particularly …
In this article, we study the bilaterally almost uniform (b.a.u.) convergence of weighted averages of a positive Dunford-Schwartz operator on the noncommutative $L_p$-spaces associated to a semifinite…
We prove that the unit group of a non-discrete irreducible, continuous ring, in the sense of John von Neumann, does not admit any non-trivial unitary representation continuous with respect to the stro…
We analyze a three-dimensional discontinuous piecewise linear system \(Z=(X,Y)\) whose switching manifold \(\Sigma\) contains visible-visible two-fold intersection lines. Assuming that the matrices \(…
We introduce a linear map on symmetric functions that 'divides' a partition by a positive integer $k$, sending a Schur function indexed by a partition of $kn$ to a symmetric function indexed by partit…
A number of goods are called identical if they provide the same level of utility to each agent. In various real-world instances of fair division scenarios, identical indivisible items are allocated to…
We investigate the necessary and sufficient condition for the existence of good involutions of symplectic quandles, which are defined on free $R$-modules with an antisymmetric bilinear form. In partic…
We study backward stochastic differential equations (BSDEs) in infinite horizon and design efficient numerical schemes for solving them. We establish a probabilistic representation of the solution of …
This paper presents a brief overview of ravine functions using the example of the Minkowski-Cohn moduli surface from the point of view of optimization on it. Elements of representation and solution of…
Gorenstein toric contact manifolds are good toric contact manifolds with zero first Chern class that are completely determined by certain integral convex polytopes called toric diagrams. The Ehrhart p…
In 2016, Viazovska famously solved the sphere packing problem in dimension $8$, using modular forms to construct a 'magic' function satisfying optimality conditions determined by Cohn and Elkies in 20…
Spectral hypergraph theory has recently attracted considerable interest as it provides a natural framework for modeling higher-order relationships beyond classical graphs. In this setting, eigenvalues…
We consider large-scale traffic assignment problems and develop a path-based compression framework. In particular, we partition paths into major and minor paths according to a set of nominal flows and…
The numerical reconstruction of controls for nonlinear partial differential equations remains a challenging and relatively underdeveloped problem, despite the extensive literature on control theory. W…
Homotopic morphisms of $\mathbb E$-triangles in extriangulated categories are introduced. Any morphism of $\mathbb E$-triangles is a composition of homotopic morphisms. Any morphism $(\alpha_1, \alpha…
For an elliptic curve E over Q and a natural number j, Cojocaru has shown that there is an explicit constant C_E,j giving (under GRH) the density of primes p of good reduction such that the smallest i…
Let $G$ be a reductive group over an algebraically closed field of positive characteristic $p$, good for the root system of $G$. The closures of $G$-orbits in the Hilbert nullcone of the coadjoint rep…
For $0<\delta,\tau<1$ and $1\le s\le \frac{n}{n-\delta}$, we prove that for a given $s$-John domain $\Omega\subset \mathbb{R}^n$, the following Boxing inequality holds for every Lebesgue measurable …
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