Mathematics
A Tychonoff space $X$ has the two-disjoint-copies property (2DCP) if there exists a sequence $(K_n)_{n\in\omega}$ of non-empty compact subsets of $X$ such that each $K_n$ contains two disjoint subsets homeomorphic to $K_{n+1}$. Banakh,…
Most approaches for accelerating Markov chain mixing either rely on incorporating expensive geometric information in the proposals, or reduce the per-step cost of sampling via surrogate densities. We propose a localisation principle that…
We study two proximal point type methods for finding equilibrium points of pseudomonotone and strongly quasiconvex bifunctions. Extending results by A. Iusem and F. Lara, we prove the strong convergence of these methods over general…
We prove a finite-scale estimate for vortex stretching in spatially filtered three-dimensional Navier--Stokes flow. The positive near-field part of the filtered stretching is bounded by a pairwise defect of filtered vorticity directions. A…
In this paper we review the connection among continuity of the diffraction spectrum, the (uniform) vanishing of the Fourier--Bohr coefficients and the so called consistent phase frequency.
Positivstellens\"atze provide certificates of positivity for polynomials. Extending these certificates to symmetric functions, uniformly across all dimensions, presents structural challenges. For instance, the underlying domain is not…
We investigate a class of drift-based transformations between multidimensional diffusion processes. The approach allows to construct a new process whose transition probability density function (p.d.f.)\ can be expressed in a product form…
A recent breakthrough of Chen, Chen, Chen, Yin, and Zhang shows rapid mixing for Glauber dynamics for the hard-core model on random regular graphs beyond the tree uniqueness threshold. Their approach builds upon the literature of various…
We show that under a suitable additional hypothesis the restricted Zassenhaus $\F_p$-Lie algebra or the rational Magnus Lie algebra of a free amalgamated product is the free amalgamated product of the corresponding Lie algebras of the…
For an acyclic cluster algebra, the $c$-vectors are, up to sign, the real Schur roots of the associated root system. We study the two-coordinate projections $(c_v, c_w)$ of this configuration: when the difference $c_v - c_w$ is bounded the…
We consider clusters formed by a Poisson ensemble of random walk loops on the $d$-regular tree with an intensity parameter $\alpha>0$ and a killing parameter $\kappa>-1$; the latter penalizes ($\kappa > 0$) or favors ($\kappa <0$) the…
A Class-Uniformly Resolvable Design (CURD) is a resolvable design in which each parallel class has the same block structure. We study CURDS in which each parallel class contains one block of size $m$ and the remaining blocks have size $2$,…
We prove two Korovkin-type approximation theorems for sequences of positive linear operators acting on continuous functions on $[0,\infty)$. Under the assumption of pointwise convergence on suitable test functions, we establish pointwise…
Assuming the Generalized Riemann Hypothesis, we establish upper bounds of conjectural order of magnitude for shifted moments of the Dedekind zeta function associated with a finite Galois extension. This improves results of Milinovich and…
For $k\geq 1$, we prove that \[ [q^n z^s]J_k(z,q)\geq 0, \qquad (n\geq 0,\ s\in\mathbb Z) \] for the normalized Jacobi triple product tails \[ J_k(z,q) = \frac{ \sum_{j=k}^{\infty}(-1)^{j-k} q^{\binom{j+1}{2}}(z^{-j}+\cdots+z^j)}…
The term tropical pseudonorm refers to a family of (not necessarily symmetric) gauge functions that arise in tropical or idempotent geometry. An important characteristic of these gauges is their invariance under translation by a constant…
We study intersections of conjugacy classes of square matrices over a finite field with affine coordinate subspaces, or equivalently matrices in a fixed adjoint orbit with prescribed entries. Our main result treats the case of prescribed…
We introduce and study $(2,3)$-palintropic algebras, a class of commutative algebras defined by the identity $(x^{3})^2 - (x^{2})^3 = 0$. This specific relation is the simplest generator of the $2$-dimensional space of minimal-degree…
Recent numerical computations and stochastic modeling by Brevitt and Klages suggest that introducing a hole in a Pomeau--Manneville map can suppress survivor-conditioned Lyapunov stretching. We prove a deterministic renewal theorem which…
We extend the study of contact cosmetic surgeries to Legendrian knots in integer homology sphere L-spaces . We prove that the contact cosmetic surgery conjecture holds for all non-trivial Legendrian knots in this setting, with the possible…