Mathematics

The paper introduces unbounded antilinear operators on Hilbert spaces and develops their fundamental theory. In particular, we establish a closed range theorem, a polar decomposition theorem, and the convexity of the numerical range for…

Caffarelli's contraction theorem and the analogous Laplacian result in [arXiv:2411.12109, arXiv:2501.11382] are two examples of how log-Hessian bounds on probability densities yield estimates on the derivative of the corresponding Brenier…

Given a pseudo-free self-similar action of a countable group $G$ on a countable directed graph $E$ with amenable stabilizers of the vertices, we identify the exact conditions under which these stabilizers do not contribute to the ideal…

Mixed-precision methods combine low and high precision arithmetics to exploit low precision computational speed and high precision accuracy. Large ODE systems that contain many heterogeneous interactions lead to a high computational cost…

The logistic two-gene negative-feedback oscillator is locally asymptotically stable for all biological parameter values, since the trace of the Jacobian is uniformly negative. Real biological oscillators (circadian rhythms, the segmentation…

In this work, we develop a constructive method for deriving four structure relations and a fourth-order linear differential equation satisfied by Laguerre-Hahn orthogonal polynomial sequences. The method relies on a combination of structure…

We study geodesics in the Brochette first-passage percolation model, where edges on the same axis-parallel line share a common random passage time, inducing long-range dependence. We focus on the maximal transversal deviation H n of…

We present in this work a very short proof for the existence, uniqueness and smoothness in dimensions $d\leq 3$ of the system of reaction diffusion $ \partial\_t a\_i - d\_i \Delta a\_i = (-1)^i (a\_1 a\_3 - a\_2 a\_4)$, where $a\_i \geq 0$…

We classify connected finite acyclic graded quivers $Q$ for which the graded path algebra $kQ$, regarded as a formal dg algebra, is silting-discrete. We prove that $kQ$ is silting-discrete if and only if it is derived-discrete, and that…

We prove norm inflation phenomena for KdV and KP equations in negative order Sobolev spaces, in the periodic case, as well as on the whole space, on an arbitrarily large scale of negative order Sobolev spaces as target spaces. The proof…

The dynamics of two-phase flows out of mechanical and thermal equilibrium are described by a partially dissipative first-order quasilinear system with stiff interaction terms associated with fast relaxation scales. In this paper, we analyze…

We prove a tropical analogue of Cartan's second main theorem for holomorphic curves intersecting hyperplanes in general position--a setting that was not fully resolved by previous tropical Nevanlinna theory. Two versions are obtained. The…

In this paper we completely classify semifields of order $2^8=256$ containing a nucleus of order $2^4=16$. We introduce new invariants for semifields, and apply new computational techniques for calculating old invariants. Together these…

The geometrisation theorem of 3-manifolds was conjectured by Thurston the 1980s and proved by Perelman in the 2000s. This is an overview on the subject. We explain the content of the theorem and describe its effects in various situations.

The moment-sum-of-squares hierarchy provides a powerful framework for solving non-convex optimal control problems by constructing a sequence of convex semidefinite relaxations. However, when extending these methods to nonlinear partial…

In scheduling problems, deterministic task durations are often assumed. This usually does not capture reality and may lead to schedules that are not robust to (small) changes to these task lengths. The use of stochastic task durations…

Real-time hierarchical energy-sharing markets are promising to coordinate large numbers of prosumers. Still, most existing clearing methods rely on linearized or DC power-flow models and do not explicitly handle reactive power or…

Various decays of the B mesons are here used to establish the performances of an ultra-granular electromagnetic calorimeter for heavy flavour physics at an electron positron accelerator running at the Z peak. The silicon-tungsten…

In this paper, we establish optimal a priori $C^{1,\alpha}$ regularity estimates for the ratio $w = v/u$ of two solutions to the same elliptic equation $-\operatorname{div}(A \nabla u )=0$ with Lipschitz coefficients $A$, under the…

We study the small-time approximate controllability of bilinear Schr{\"o}dinger equations, where the drift is a magnetic Schr{\"o}dinger operator and the control is an electric potential. We prove this property in two circumstances: (i) in…