数学

We show the existence of a topologically free minimal action of $\mathbb F_\infty$ on the Cantor space that does not have dynamical comparison. Moreover, we show that this phenomenon can happen both in the presence and in the absence of…

A defending state facing sustained economic, media, and psychological pressure from an adversary that continuously re-optimises its campaign poses a problem that existing attacker-defender models in operations research do not directly…

Classical equivariant bordism theories require computing the full collection of equivariant characteristic numbers to detect whether an equivariant manifold bounds equivariantly or not. This paper establishes simplified equivariant bordism…

We develop a variational nonlocal phase-field model for dynamic fracture in elastic solids. The proposed formulation is distinguished by three main features. First, the model is formulated through nonlocal kinematics and kernel-dependent…

Let $W$ be an even Coxeter group. We prove that among all Coxeter systems generating $W$ the unique even Coxeter system realizes the minimal exponential growth. Our proof relies on comparing the exponential growth rates in the explicit…

Let $G$ be the orbifold fundamental group of the moduli space of smooth cubic surfaces $\mathcal{M}_{\mathsf{sm}}$ in $\mathbb{P}^3_{\mathbb{C}}$ with base point at the Clebsch surface $X_{\mathbf{1}}$. The image of the monodromy action $G…

We consider locally compact L{\'e}vy trees conditioned to be large, with respect to different criterion: its height, its maximal ''size'' vertex and its total ''mass''. In the critical case, we provide a coupling with a truncated Kesten…

We partially answer two open questions concerning diameter two properties in absolute sums. First, we identify the conditions that a super $\Delta$-point in an absolute sum of Banach spaces imposes on the coordinates. Secondly, we show that…

We show that the language of geodesic words representing elements of a stable subgroup $H$ of a group $G$ with finite generating set $A$ is regular, and that there is a sublanguage which bijects $H$. Consequently, the growth function of $H$…

We compute the tensor of the multiplicative group scheme with the mod-$2$ motivic cohomology spectrum in normed motivic spectra over the complex numbers, and find that the resulting algebra is free on a generator in bidegree (2,1). This…

This article investigates the long-time behavior of (possibly infinite-dimensional) impedance passive systems under saturated output feedback and external disturbances. We assume that, in the absence of saturation and disturbances, the…

We study the Cauchy problem associated with a class of triangular cross-diffusion systems of Shigesada-Kawasaki-Teramoto type. We develop a self-contained well-posedness theory in C 0 ([0, T ]; H s (T d )) based on regularity estimates for…

We prove global existence for a degenerate Keller-Segel equation with small initial values in a critical Lorentz space.

We establish an analogue of the Brezis-Nirenberg local linking theorem for a class of Szulkin-type functionals arising from relativistic action principles. In this framework, compactness of Palais-Smale sequences is formulated with respect…

We study the one-time weight on strict partitions obtained from the modified odd Greaves--Jing--Zhu operator. The shifted $t$-Schur functions generated by this operator are obtained from the classical Schur $Q$-functions by the plethystic…

We prove a new polynomial upper bound for the Lebesgue constants of $\tau$-Leja sequences on finite unions of real intervals. Building on an estimate of Andrievskii and Nazarov, we replace the global separation of the first $n$ Leja points…

Let $\Gamma$ be a complex reflection group acting on the complex affine or hyperbolic space $X$ with the set of reflecting hyperplanes $\mathcal{H}$. We define an augmented rack $(G, \mathcal{K}, p)$ associated to the orbifold fundamental…

This article develops a tangential arc-space approach to foliated discrepancies for logarithmic simple co-rank one foliations on threefolds, relative to a fixed invariant normal-crossing separatrix divisor. In the non-resonant logarithmic…

We prove the finite-time stability of two-soliton solutions of the three-dimensional gravitational Hartree equation whose centers remain close to an elliptic solution of the Kepler two-body problem.

M. Gorelik and Th. Heidersdors in the papers \cite{GH} investigated Euler characters for Lie superalgebra $\frak{gl}(m,n)$ and $\frak{osp}(m.2n)$. In the present paper we also investigate Euler characters for Lie superalgebra…