arXiv preprints from January 1, 2026 through September 8, 2026 — 04:59:04 EST
We establish the global existence of forward self-similar solutions to the two-dimensional incompressible Navier-Stokes equations for any divergence-free initial velocity that is homogeneous of degree $-1$ and locally Hölder continuous. This result requires no smallness assumption on the initial data. In sharp contrast to the...
We investigate relationships between polar/polynomial solutions to the double shuffle relations modulo products, which were independently introduced by Brown and Ecalle.
This paper investigates residue maps and their spanning properties for singular algebraic curves, with particular emphasis on three interconnected themes: the \emph{scheme--theoretic residue span}, the \emph{residue--balancing principle}, and \emph{residue balancing in the presence of arbitrary singularities}. Starting from the theory...
We develop a general incremental framework for hyperelastic solids whose surfaces exhibit both stretch-dependent and curvature-dependent elastic behavior. Building upon a variational formulation of curvature-dependent surface elasticity, we derive compact governing equations expressed in a coordinate-free Lagrangian setting that...
In large-scale Bayesian inverse problems, it is often necessary to apply approximate forward models to reduce the cost of forward model evaluations, while controlling approximation quality. In the context of Bayesian inverse problems with linear forward models, Gaussian priors, and Gaussian noise, we use perturbation theory for...
The Schur multiple zeta function was defined as a multivariable function by Nakasuji-Phuksuwan-Yamasaki. Inspired by the product formula of Schur functions, the products of Schur multiple zeta functions have been studied. While the product of two Schur functions expands as a linear combination of Schur functions, it is known that a...
The paper is concerned with a nonlinear system of two coupled fractional Schrödinger equations with both attractive intraspecies and attractive interspecies interactions in $\mathbb{R}$. By analyzing an associated $L^2$-constrained minimization problem, the uniqueness of solutions to this system is proved via the implicit function...
In this paper we investigate the influence of the discretization of PDE constraints on shape and topological derivatives. To this end, we study a tracking-type functional and a two-material Poisson problem in one spatial dimension. We consider the discretization by a standard method and an enriched method. In the standard method we...
Starting from the following multidimensional integrable generalizations of the heavy rigid body systems: the Euler top, the Lagrange top, the Lagrange bitop, and the totally symmetric case, we add to each of them a gyroscope. For each of the newly constructed systems, we provide a polynomial matrix Lax representation and prove...
Associated to a Lie groupoid, there are two $C^*$-algebras: the full and the reduced one. The associated order $0$ pseudodifferential calculus gives rise to multiplier algebras of both. We prove that both associated corona algebras are equal to the natural (commutative) principal symbol algebras.
We develop a relative boundary theory for actions of discrete groups on compact spaces and use it to derive rigidity results for reduced crossed products. For a discrete group $Γ$ acting on a compact space $X$ and a subgroup $H$, we construct a universal boundary over $X$ which is minimal as a $Γ$-system and strongly proximal with...
In this work, we study a numeral system with a natural base $s \geq 2$ and a redundant alphabet $A_r=\{0,1, \dots, r\}$, where $s \leq r \leq 2s-2$. We investigate the topological, metric, and fractal properties of the set of numbers in the interval $\left[0,\frac{r}{s-1}\right]$ that admit a unique representation...
Let $G=G_1 \ast \ldots \ast G_k \ast F_N$ be a free product of finitely presented groups, where $F_N$ is a free group of rank $N \in \mathbb{N}$. Let $\mathrm{Out}(G,\mathcal{G})$ be the subgroup of $\mathrm{Out}(G)$ preserving the set of conjugacy classes $\mathcal{G}=\{[G_1],\ldots,[G_k]\}$. Under natural conditions on the groups...
We consider the densest submatrix problem, which seeks the submatrix of fixed size of a given binary matrix that contains the most nonzero entries. This problem is a natural generalization of fundamental problems in combinatorial optimization, e.g., the densest subgraph, maximum clique, and maximum edge biclique problems, and has wide...
This study investigates the connection between boxed UC plane partitions and the two-site generalized phase model. By introducing two maps, we investigate the representation of two-side generalized phase algebras and actions of monodromy matrix operators on basis vectors. The generating function of boxed UC plane partitions is...
Finding constrained saddle points on Riemannian manifolds is significant for analyzing energy landscapes arising in physics and chemistry. Existing works have been limited to special manifolds that admit global regular level-set representations, excluding applications such as electronic excited-state calculations. In this paper, we...
This paper addresses the nonparametric estimation of a spatially varying, heteroskedastic variance function on the unit sphere within a regression framework. While adaptive regression estimation is well-established on manifolds, characterizing localized noise structures presents unique theoretical obstacles due to bias propagation...
We study the expansions of permutation statistics in the basis of functions counting occurrences of a fixed pattern in a permutation. We show the finiteness of these pattern expansions for a class of permutation statistics including the higher moment statistics, generalizing a result of Berman and Tenner. We also give a combinatorial...
Presentaremos una nueva demostración del teorema de Shafarevich sobre finitud de curvas elípticas con buena reducción fuera de un conjunto finito de primos dado. Esto da un nuevo punto de entrada a teoremas fundamentales de finitud diofantina tales como el teorema de Siegel sobre la ecuación $S$-unidad. Nuestro argumento está libre de...
We study the mutual singularity of countable Gaussian mixture models (GMMs), with particular emphasis on infinite-dimensional settings. We first establish that a countable mixture of Gaussian probability measures is itself a well-defined probability measure. We then prove a general measure-theoretic result showing that if every...
Geometric and Topological Deep Learning are rapidly growing research areas that enhance machine learning through the use of geometric and topological structures. Within this framework, Group Equivariant Non-Expansive Operators (GENEOs) have emerged as a powerful class of operators for encoding symmetries and designing efficient,...
The classical Mazur-Ulam theorem establishes that every surjective isometry between normed real vector spaces is an affine transformation. In various applied mathematical settings, however, one encounters maps that preserve distances not pointwise, but almost everywhere with respect to a probability measure. This paper provides a...
We prove the AKSZ theorem for shifted Poisson structures: if $X$ is an $n$-shifted Poisson derived stack, and $Y$ a $d$-oriented derived stack, then the mapping stack \[\underline{\mathrm{Map}}(Y,X)\] is naturally endowed with an $(n-d)$-shifted Poisson structure. For this, we prove that the data of an $n$-shifted Poisson structure on...
We exhibit an explicit family $\mathcal{B}$ of $30$ subsets (``blocks'') of size $6$ of $[60]=\{1,2,\dots,60\}$ with the following property: for every $6$-subset $S\subset[60]$, there exists a block $B\in\mathcal{B}$ such that $|S\cap B|\ge 2$. The construction is fully explicit and the proof is purely combinatorial.
We show that the derived category of complexes with quasi-coherent cohomology on a regular Noetherian algebraic stack with quasi-finite diagonal is generated by a single perfect complex. In the concentrated case, the category is singly compactly generated. Key ingredients in the proofs include gluing generators along recollement and...