Mathematics
The aim of this article is twofold: (a) to revisit the blow-up theory of weakly superlinear heat equations; (b) to explore the notion of internal global/regional blow-up controllability for the linear heat equation.
We compute invariants of Carrollian spacetimes, deriving them from the geometry of the screen bundle. For generic Carrollian structures we specify how to generate the entire algebra of differential invariants, with emphasis on dimension 3,…
Signed measures are traditionally introduced as countably additive set functions that may take both positive and negative values. The classical Jordan decomposition theorem shows that every finite signed measure can be expressed uniquely as…
A graph $G$ is $(t+1)K_{r+1}$-free if it contains no $t+1$ pairwise vertex-disjoint copies of $K_{r+1}$. Moon [Canad. J. Math. 20 (1968) 95-102] and Simonovits [Theory of Graphs (Proc. Colloq., Tihany, 1966)] independently determined that,…
In this paper, we study how partial observability and inexact latent-state inference affect reward learning from preferences. To that end, we study preference-based reward learning under partial observability, where the learner forms…
In this paper, we focus on the four-dimensional Thurston geometries whose isometry groups are four-dimensional, namely $\mathrm{Sol}_1^4$, $\mathrm{Sol}_{m,n}^4$ and $\mathrm{Nil}^4$. We classify homogeneous hypersurfaces in the above three…
We extend the notion of computads for weak \(\omega\)-categories to allow marking certain generators as invertible, and describe inductively the free \(\omega\)-categories they generate. This gives a simple, finite description of the…
We investigate a regularized Newton method for unconstrained convex multi-objective optimization with twice continuously differentiable objectives whose Hessians are Lipschitz continuous. At each iteration, the method minimizes the…
Perel'man in 1987 and independently Pukhov in 1979 proved that the quotient between the $(n-i+1)$-th successive outer radius and the $i$-th successive inner radius of a convex body in $n$-dimensions is not larger than $i+1$. Apart from the…
We determine the continuous mod $p$ homology of the topological periodic homology $TP(MU)$ of the complex cobordism spectrum, as a graded algebra with Steenrod operations. The answer is given in terms of an explicit and purely algebraic…
The stabilizing effect of a background magnetic field on electrically conducting fluids has been rigorously established for the standard MHD equations. This paper extends this theory to the more physically accurate damped wave-type MHD…
In this paper, we study the congruence $\binom{qn}{n} \equiv q^n \pmod n$ for a prime base $q$. Motivated by the OEIS sequence \seqnum{A080469} and the conjectural existence of infinitely many ternary solutions of the form $n=3^t p$, we…
Learned reconstruction operators for inverse problems are typically trained under a fixed noise model, and generalize poorly when the distribution during testing differs from the one assumed during training. Distributionally robust…
Valid possibilistic inferential models provide exact finite-sample calibration, but validity alone does not determine which valid procedure results in the most informative inferential summary. This paper proposes Choquet risk as a…
Sudoku is a compact and familiar setting for teaching a surprisingly deep lesson in integer linear programming, namely that the most natural decision variables are not always enough to produce an effective or convenient linear model. This…
A new, fast adaptive regularization methods is proposed and analyzed under local Lipschitz smoothness of the $p$-th order tensor. For nonconvex problems, it achieves the optimal…
We consider the defocusing Wick-ordered cubic fractional nonlinear Schr\"odinger equation on the two-dimensional torus with dispersion relation $\omega(k)=|k|^\alpha$. In the weakly dispersive regime $\frac{29}{15}<\alpha<2$, we construct…
In this work, we study the nonlinear orbital stability of solitary-wave solutions for a class of higher-order Boussinesq systems with Hamiltonian structure. Using variational methods and the asymptotic connection with generalized…
We study the two-color distinct-part series \(S_1(q)\), equivalently Andrews' generating function \(v_d(q)\) for strictly concave compositions, and its odd and even companions \(T_o(q)\) and \(T_e(q)\). We determine the coefficients of…
We study travelling-rotating solutions of the Schr\"odinger map equation into the sphere, viewed as tangent profiles of rigid vortex filaments. Two first integrals reduce the profile equation to a scalar cubic equation for the vertical…