Mathematics
This first part of the series builds the analytic layer of noncommutative anisotropic diffusion in a separable Hilbert space. Let $\mu_0=\mathcal{N}(0,Q)$ be the reference Gaussian measure, with $Q\in L^1(\mathcal{H})$, and let $D(x)$ be a…
We establish Liouville-type theorems for the stationary fractional Navier-Stokes equations in $\mathbb{R}^n$ under suitable integrability conditions on the velocity field $u$ and a large-scale Morrey-type bound on the fractional energy. As…
In this paper, we provide an integration by parts formula for plurisubharmonic functions on a hyperconvex domain that are bounded outside a compact set. This extends a previous result of Urban Cegrell.
In the paper we describe hyperbolic surfaces filled by their systoles, where the total number of systoles is in $O(\frac{g}{\ln \,g})$, that is equivalent to the lower bound of Anderson, Parlier and Pittet \cite{APP}. Various papers…
This paper focuses on the regularity of viscosity solutions to normalized $p$-Laplacian equations with variable-exponent double phase type degeneracy/singularity and Hamiltonian terms. Based on a new improved oscillation-type estimate…
In this paper, we study a quantitative Runge-type global approximation theorem for the linearized magnetohydrodynamic (MHD) system in bounded domains with arbitrary topology. In the context of magnetic relaxation, the interplay between the…
The hydrodynamic limit to the barotropic Euler equations, including power-law pressure $P(\rho)=\rho^\gamma$, for a kinetic nonlinear Fokker--Planck equation with degenerate diffusion is established. This extends the well-known result of…
We propose and analyze a space-time discontinuous Galerkin method for the incompressible Stokes equations on moving domains within the arbitrary Lagrangian-Eulerian setting. We use a contravariant Piola map in the definition of the discrete…
In this paper, we consider distributed parameter estimation with binary observations under measurement-side tampering: each node observes a thresholded output whose label may be flipped and exchanges information over a communication graph.…
This paper establishes a pointwise gradient potential estimate for solutions to linearized Monge-Amp\`ere equations and derives a modulus of continuity estimate for the gradient in terms of the associated section adapted potential. As…
We study doppelsemigroups, i.e., algebraic structures equip\-ped with two associative binary operations satisfying a specified system of axioms. We investigate duality and isomorphisms of doppelsemigroups and examine the relationships…
A subgraph $H$ of $G$ is said to be $F$-saturated relative to $G$, if $H$ does not contain any copy of $F$, but the addition of any edge $e$ in $E(G)\backslash E(H)$ would create a copy of $F$. The minimum size of an $F$-saturated graph…
Let $(M^n,g)$ be a complete Riemannian manifold of dimension $n\geq 5$ endowed with a critical metric of the quadratic scalar-curvature functional $$ \mathcal S^2(g)=\int_M R_g^2\,dV_g . $$ For $n\geq 10$, Catino, Mastrolia and Monticelli…
We investigate linear lumping for parameter-dependent mass action reaction networks, distinguishing between generic and critical parameter regimes. For generic parameters -- those ranging in some non-empty open subset of parameter space --…
In this paper, we study the so-called log-convergence of graphs defined by Bal\'azs Szegedy (arXiv:1504.00858). We answer his Question 4 affirmatively: the sequence of incidence graphs of projective planes over finite fields log-converges,…
We study a mean-field optimal control problem for a consensus (high-dimensional Kuramoto-type) dynamics with diffusion on the unit sphere. The control acts through a prescribed drift field and an interaction gain, and the cost functional is…
The paper considers the Cauchy problem for a first-order integro-differential equation with memory in a finite-dimensional Hilbert space. The main computational difficulty of such problems is the need to store and process the solution at…
In this paper, we prove a Dolbeault geometric Langlands equivalence for $\GL_r$ and for the Langlands dual pair $\SL_r/\PGL_r$ over an open locus of the Hitchin base which strictly contains the elliptic locus. This open locus contains the…
In periodically forced dynamical systems, resonance tongues are open regions of a parameter plane in which the dynamics on an invariant torus locks to a stable periodic orbit. While individual resonance tongues are well understood, the…
This paper develops a path-first theory using the signature as a universal coordinate for deterministic paths, rough paths, jump streams, and path-valued random variables. Geometricity is presented as a first-order algebraic property with…