Research
Research
Research
Research
1,124+ open-access research outputs.
Paul Erdos posed the following question: Is there a prime number $p>5$ such that the residues of $2!$, $3!$,\ldots, $(p-1)!$ modulo $p$ all are distinct. In this short note, we give the negative answe…
This paper introduces the separable covariance mixture model, which assumes a data-matrix $Y$ to be of the form $$ \sum\limits_{r=1}^R A_r X B_r $$ for one random $(d \times n)$-matrix $X$ with indepe…
We compute the cohomology groups of the pure symmetric outer automorphism group $\Sigma$POut$(A_\Gamma)$ and the pure symmetric automorphism group $\Sigma$PAut$(A_\Gamma)$ of a right-angled Artin grou…
The LogQ algorithm encodes Quadratic Unconstrained Binary Optimization (QUBO) problems, which are often encountered in the industry (portfolio optimization, fleet optimization, charging stations, etc.…
In this paper we prove that if a closed set in R^N is close to a cone over a simplicial complex at each point and at each scale, then it is locally bi-H\"older equivalent to such a cone. This generali…
In this paper, we study the almost everywhere convergence of the cubic nonlinear Schr\"odinger flow to the initial data on $\mathbb S^2$, \begin{equation*} iu_t + \Delta_g u = |u|^2u, \quad (t,x)\…
This tutorial contrasts probabilistic modeling and robust optimization to determine decisions in humanitarian logistics, specifically supply chains subject to adversarial (natural and human) disruptio…
We study the stabiliser formalism for qudits of arbitrary dimension $d$. In the free case, we show that the basic theorem of the stabiliser formalism remains valid: if the stabiliser subgroup $H$ is f…
This paper is concerned with finite-level quantum memory systems for retaining initial dynamic variables in the presence of external quantum noise. The system variables have an algebraic structure, si…
In this paper, a three-dimensional competitive Lotka-Volterra system with four limit cycles is constructed for class 28 in Zeeman's classification. Combined with existing results -- from Gyllenberg an…
We continue the study of Dow spaces of a $\mathfrak{b}$-scale, originally introduced by Alan Dow in "$\pi$-Weight and the Fr\'echet-Urysohn property" (Topology and its Applications, Vol. 174, pp. 56-6…
We show that the Bergman kernel of a finite-volume quotient of a Hermitian manifold $\widetilde{X}$ with bounded geometry by a discrete group $\Gamma$ of its isometries is the same as the averaging ov…
In this article, we establish an analogue of Pitt's inequality for the Strichartz Fourier transform on the Heisenberg group $\mathbb{H}^n$. By exploiting the scalar-valued formulation of the transform…
Let $\mathbb{Z}$ be the additive group of all integers and $\mathbb{N}$ the sub-monoid of $\mathbb{Z}$ of all non-negative integers. For a finite subset $X$ of $\mathbb{Z}$, we denote by ${\rm max}\ X…
Let $(X,\omega_0)$ be a compact K\"ahler manifold and $\mathcal X\to B$ its Kuranishi family, where the base $B$ may be singular with $\dim_{\C} B \ge 1$. Using explicit sections of Hodge bundles obta…
In this paper, we are concerned with the Cauchy problem for the generalized KdV equation with random data and rough data. Firstly, when $s\in\mathbf{R}$, by using the initial value randomization techn…
The purpose of this article is two-folds. Firstly, we establish two sufficient conditions under which the sequence $\{f(n)\pmod{m}: n\geq1\}$ is non-periodic, where $f(n)$ is an arithmetic function. A…
This paper investigates the isomorphisms between principal distributions $\mathcal{D}_k$ $(k=1,\dots 4)$ on OT--FKM type isoparametric hypersurfaces in spheres. We recover the isomorphism $\mathcal{D}…
The gap between high school and university level mathematics has long been deemed problematic. Felix Klein referred to this gap as the ''double discontinuity'' meaning that students come to university…
It is proved by M. Paun (1997, 2017) that the fundamental group of a compact Kahler manifold X is almost Abelian if the anti-canonical bundle -KX is nef. In this paper, we apply the recent geometric a…
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