Mathematics

Let A be an n x n Bernoulli random matrix whose entries are i.i.d. Bernoulli(p) random variables. In this paper, we determine the probability that the corank of A is at least k when k is of order O(sqrt(log n)): P(corank A >= k) =…

We propose and analyze a nonstandard finite difference (NSFD) scheme for nonlinear parabolic equations involving a p-Laplacian-type diffusion operator in one- and two-dimensional spatial domains. Following Mickens' design principles, the…

Based on the growth patterns of 166 CHO monoclones observed over a 15 day period, we show that the standard population growth in a confined space equation, i.e. the sigmoid/logistic function, is alone does not capture the complex behaviour…

Using a variational approach, we study the existence of periodic solutions with prescribed energy for the relativistic equation \begin{equation*} \dfrac{\mathrm{d}}{\mathrm{d}t}\left(\dfrac{m\dot x}{\sqrt{1-|\dot{x}|^{2}/c^{2}}}\right) =…

We study existence, regularity, and uniqueness for the nonlinear kinetic Fokker--Planck equation $$ \partial_t f=\Delta_v\Psi(f)-v\cdot\nabla_x f, \qquad f|_{t=0}=f_0, $$ on $\mathbb R^{2d}$. In the model case $\Psi(r)=r^s$, this equation…

Let $\mathcal Q=\{Q_a:a\geq1\}$ be a nested family of finite posets such that $Q_a\subseteq Q_{a+1}$ and $|Q_a|<|Q_{a+1}|$. For a poset $Q$, let $\mathcal C_t(Q)$ denote the set of all strict $t$-chains in $Q$. Given an $r$-coloring of…

This paper proposes an inner--outer (IO) iterative algorithm with optimal parameters for solving stochastic Lyapunov matrix equation associated with discrete-time stochastic linear system. First, under the assumption that the underlying…

We consider the free boundary problem for the Euler equations of fluid dynamics governing the motion of a 3D liquid drop with capillarity $\sigma_0$ and nearly spherical shape, under the assumption of constant vorticity $(0, 0, \alpha_0)$.…

Tall complexity one $T$-spaces are Hamiltonian $T$-spaces $(M,\omega,\Phi)$ such that $\frac{1}{2}\dim M -\dim T=1$ and the symplectic quotient at each moment value is a surface. The skeleton of a complexity one $T$-space is an important…

We introduce and study a subalgebra $\mathcal{B}$ of the affine Hecke algebra, which arises from a centralizer construction in the double affine Hecke algebra, and which may be regarded as a $v$-deformation of the affine Fomin-Stanley…

Classical summation methods are often organized around particular growth regimes. Standard Borel summation is suited to Gevrey-1 series, while higher-order Gevrey behavior is commonly handled by changing the kernel, for instance through…

We extend the Susceptible--Addicted--Reformed (SAR) model of \cite{sanchez2023}, which exhibits a forward--backward bifurcation driven by nonlinear relapse, by embedding an epi-economic behavioral layer in the spirit of \cite{fenichel2011}.…

The question of whether a ring is additively generated by its units has been studied from several perspectives in ring theory and algebraic graph theory. In this paper, we investigate this problem for finite rings, not necessarily…

In this paper, we study local (anti-)superderivations on finite-dimensional nilpotent Lie superalgebras. Firstly, we prove that every finite-dimensional 2-step nilpotent Lie superalgebra over a field $\mathbb{F}$ with…

Trajectory-based learning of dynamical systems is often fragile in the presence of noise, chaos, or sparse observations, as small pointwise errors can rapidly amplify. We introduce a transition-statistics approach to system identification…

We study resonance phenomena in the periodically forced Suarez--Schopf delay differential equation, which is a conceptual climate model for the El Ni\~no--Southern Oscillation (ENSO). The system serves as a prototypical forced…

The parareal algorithm is one of the most widely studied parallel-in-time methods for the numerical approximation of time-dependent problems. For non-diffusive equations, however, standard parareal methods may converge slowly or even become…

This paper develops a contraction-based stability analysis for regularized model predictive control (MPC), whose feedback law is defined implicitly by a finite-horizon optimal control problem with an additional regularizing cost. The…

In this paper we propose a novel physics-informed neural network framework for solving general first-order delay differential equations. Our approach combines a differentiable history switch, a trial-solution formulation that explicitly…

We study finite-field analogues of the Peres--Schlag nonempty-interior problem for product sets. Given \(A\subseteq\mathbb F_p\), we ask when a suitable one-dimensional linear image of \(A^n\) is full; equivalently, when there exist…