Mathematics

We investigate the influence of routing strategies and speed limit policies on optimal solutions in traffic emission models. Building on a first-order macroscopic traffic model coupled with an advection-diffusion model, we formulate single-…

In this paper, we classify all solitons of the Gauss curvature flow in the three-dimensional Heisenberg group $\mathrm{Nil}_3$ that are invariant under a one-parameter group of ambient isometries. By means of the four canonical types of…

Bergeron, Garsia, Haiman and Tesler conjectured in 1999 that, for all partitions $\mu,\lambda\vdash n$, the polynomial $(-1)^{|\mu|-\ell(\mu)}\langle \nabla m_\mu, s_\lambda\rangle$ has nonnegative integer coefficients, where $\nabla$ is…

We resolve (for all sufficiently large $n$) a conjecture of Pilz on the symmetric difference $A\Delta (2A)\Delta \cdots\Delta (nA)$ for finite sets $A\subseteq \mathbb{N}$ of positive integers. We show that this set always has cardinality…

Let $p$ be an odd prime and let $V_{k,a_p}$ be the two-dimensional crystalline representation of the Galois group of ${\mathbb Q}_p$ of weight $k \geq 2$ and parameter $a_p \in \bar{\mathbb{Q}}_p$. We study the semi-simplification…

This paper proposes a direct inversion method for the 2D type-II nonuniform discrete Fourier transform~(NUDFT). The NUDFT matrix $A$ is factored as $A = G F$, where $G$ can be expressed as a kernel matrix and $F$ is the 2D DFT matrix. We…

Order polytopes for generalized snake posets were recently studied by von Bell et al. (2022), and are known to be unimodularly equivalent to strength-one flow polytopes for acyclic directed graphs strongly dual to generalized snake posets.…

Model order reduction techniques have become an attractive approach for obtaining fast approximations of multidimensional problems. Besides computational efficiency, ensuring the reliability of the resulting approximations is of primary…

We study the three-dimensional incompressible free-boundary ideal magnetohydrodynamic (MHD) equations with surface tension and a closed free surface. Our first result establishes $H^3$ a priori estimates in general bounded domains, without…

This paper considers the unconstrained minimization of a lower semicontinuous function. Exploiting first and second subderivatives, directional limiting subdifferentials, and directional proximal subdifferentials, necessary and sufficient…

W}e study the equation $P(i\nabla)u=0$ on $\mathbb{R}^d$ for a class of admissible symbols $P$ whose zero set is the unit sphere $S^{d-1}$ and which vanish there to some finite order. Working in the framework of Lizorkin distributions, and…

We investigate the class of measures of finite energy integrals and the behavior of potentials and co-potentials associated with non-symmetric closed forms. In particular, we compare these objects with their symmetric counterparts from…

We consider the problem of designing input signals for an unknown linear time-invariant system in such a way that the resulting data, within a finite horizon, is suitable for identification with a desired accuracy. We consider both…

Schwarz type domain decomposition methods generally require a partition of unity to combine solutions on subdomains. However, in mesh-based methods it is common to organize subdomains with minimal overlap, if any, which is facilitated by…

Let $G$ be a graph and $I(G)$ its edge ideal. The $p$-th squarefree power $I(G)^{[p]}$ is the monomial ideal generated by squarefree monomials corresponding to the matchings of size $p$ of $G$. In this paper, we provide a combinatorial…

Hybridizable staggered discontinuous Galerkin methods are developed for arbitrary-order polyharmonic equations $(-\Delta)^m u=f$ on shape-regular polytopal meshes in $\mathbb R^d$, for any $m\ge1$, $d\ge2$, and polynomial degree $k\ge0$.…

We determine the minimal absolute value of a non-vanishing sum of $n$ fifth roots of unity chosen with repetition, and characterize the corresponding sums. As a function of $n$, the minimal absolute value is monotone non-increasing over…

This paper investigates the Hurwitz existence problem for rational maps with three branch points. We establish several new families of realizable branch data and identify previously undocumented exceptional data. This work constitutes the…

We introduce the lower and upper Wythoff-Fibonacci sequences, obtained from the classical Wythoff sequences by a Fibonacci correction. Specifically, if we put $$\epsilon(j)=\begin{cases}(-1)^k, & \text{if }j=F_k\text{ for some }k\\ 0, &…

We study a notion of fractional $s$-mass for codimension-two currents on closed Riemannian manifolds, defined via energy minimization with a prescribed Jacobian constraint. We prove equi-coercivity and $\Gamma$-convergence, with respect to…