Mathematics

Body-fitted finite-element methods deliver high-order accuracy but hinge on a clean, watertight, conforming mesh, a requirement that breaks down for the geometrically imperfect CAD assemblies, image-based volumetric data, and voxel-native…

We consider species, consisting of a possibly infinite set of rings, and bimodules between them. Simson realised the category of representations as a functor category, which we prove is hereditary when each of the rings is semisimple. We…

In the context of hyperbolic formulations of Einstein's field equations obtained via gauge fixing, constraint damping is a desirable feature that ensures that violations of the gauge condition and thus of the constraint equations are…

We study the shadowing property for continuous endomorphisms of locally compact groups, using the left uniformity. For Lie groups we obtain a complete infinitesimal characterization: an endomorphism has shadowing if and only if its…

We study the two-dimensional stochastic Navier-Stokes equations on the torus with horizontal dissipation and additive noise. First, we prove a uniform large deviation principle for the solution paths in the energy space $C([0,T];H).$ The…

The well-posedness of multidimensional quadratic backward stochastic differential equations (qBSDEs) remains one of the central open problems in BSDE theory. Motivated by a mean-field utility maximization model with price impact, we…

We establish new connections between real and complex contact geometry via embeddings of 3-manifolds into $\C^3$. We introduce a new \emph{contact wedge} construction combining two transverse real contact structures to make a new…

We study the stability, tracking, and convergence of nonautonomous systems with time-varying nonisolated equilibrium sets. A Lyapunov framework based on coupled dissipation channels is developed to analyze the evolution of trajectories…

This work introduces and studies strong affine semigroups, extending the notion of strong numerical semigroups to the higher-dimensional setting. We show that non-numerical strong affine semigroups present structural differences with…

We describe an artistic project consisting of fabricating the 3532 different soccer balls that can be obtained by randomly assembling the 32 pieces of a classic Telstar soccer ball.

In 1976, J. H. Conway introduced Nim arithmetic which establishes an algebraically closed field structure over the class of ordinals and proved that the first transcendental ordinal is $\omega^{\omega^\omega}$. The problem of finding the…

Let $R(z)=\sum_{n=0}^{\infty} r_n z^n$ be a power series with $|r_n|=1$ for every $n\ge 0$. We show that for each integer $m\ge 2$, the coefficient sequence of $R(z)^m$ is unbounded. The proof combines Parseval's identity with Jensen's…

We study finite-horizon Markov Decision Processes (MDPs) under distributional uncertainty in the transition kernels and develop a policy-gradient framework for Wasserstein distributionally robust control. Ambiguity is modeled by…

We study a one-dimensional active-line equation arising as a thin-sheet reduced mechanism for high-Weissenberg Oldroyd-B dynamics. The unknown is a positive periodic line density rho=m+eta satisfying rho_t+c rho Lambda rho-c(H…

We study the stability of a classical family of metrics defined over functions' Gaussian scale-space representations, focusing on the comparison of images (functions of two variables). These metrics have precedents both in harmonic…

Power system planning models provide important guidance on long-term investment strategies with significant socio-economic impact. To remain computationally manageable, however, such planning models compromise on the level of complexity…

In this article, we derive explicit formulae expressing multiple orthogonal polynomials in terms of standard orthogonal polynomials. We treat both the real-line and unit-circle settings: multiple orthogonal polynomials on the real line…

This paper investigates the topological properties of intersections of balls in finite-dimensional normed spaces - a problem that naturally arises when constructing covers for estimating the Gromov-Hausdorff distance. We study the topology…

We introduce a new model for $(\infty,n)$-categories as Segal sheaves on lax grids, which are pasting diagrams of lax cubes. This model allows for a direct construction of the Gray tensor product via Day convolution. We show that this…

We study maximum-drawdown laws conditioned on extremes for a spectrally negative L\'evy process and observed up to an independent exponential time. The main contribution is a set of scale-function characterizations of the pre-infimum path…