Related papers: Multi-recurrence and van der Waerden systems

We present a unified understanding of the experimentally observed minimal dc conductivity in weakly disordered graphene. Firstly, based on linear response theory, we reveal that randomness or disorder inevitably induces momentum dependent…

We explain in depth the previously proposed theory of the coherent Van der Waals(cVdW) interaction - the counterpart of Van der Waals (VdW) force - emerging in spatially coherently fluctuating electromagnetic fields. We show that cVdW…

We discuss "Banach SN spaces", which include Hilbert spaces, negative Hilbert spaces, and the product of any real Banach space with its dual. We introduce "L-positive" sets, which generalize monotone multifunctions from a Banach space into…

We derive electronic structure models for weakly interacting bilayers such as graphene-graphene and graphene-hexagonal boron nitride, based on density functional theory calculations followed by Wannier transformation of electronic states.…

For different classes of measure preserving transformations, we investigate collections of sets that exhibit the property of lightly mixing. Lightly mixing is a stronger property than topological mixing, and requires that a lim inf is…

In this paper, we prove new existence and multiplicity results for critical points of lower semicontinuous functionals in Banach spaces, complementing the nonsmooth critical point theory set forth by Szulkin and avoiding the need of the…

We investigate the shrinking target and recurrence set associated to non-autonomous measure-preserving systems on compact metric spaces, establishing zero-one criteria in the spirit of classical Borel-Cantelli results. Our first main…

The phenomenon of turbulence is investigated in the context of globally coupled maps. The local dynamics is given by the Chat\'e-Manneville minimal map previously used in studies of spatiotemporal intermittency in locally coupled map…

In this paper we consider the "quasidensity" of a subset of the product of a Banach space and its dual, and give a connection between quasidense sets and sets of "type (NI)". We discuss "coincidence sets" of certain convex functions and…

We present a novel notion of $\lambda$-monotonicity for an $n$-species system of partial differential equations governed by mass-preserving flow dynamics, extending monotonicity in Banach spaces to the Wasserstein-2 metric space. We show…

We present necessary and sufficient conditions on systems of random variables for them to possess a lacunary subsystem equivalent in distribution to the Rademacher system on the segment [0,1]. In particular, every uniformly bounded…

In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems,…

We introduce the post-processing preorder and equivalence relations for general measurements on a possibly infinite-dimensional general probabilistic theory described by an order unit Banach space $E$ with a Banach predual. We define the…

In this paper a fluid-structure interaction problem for the incompressible Newtonian fluid is studied. We prove the convergence of an iterative process with respect to the computational domain geometry. In our previous works on numerical…

Let $X$ be a real Banach space and let $Y \subseteq X^*$ be a linear subspace having the Orlicz-Thomas property, that is, for each $\sigma$-algebra $\Sigma$ and for each map $\nu:\Sigma\to X$, the countable additivity of the composition…

Complex analysis is a powerful tool to study classical integrable systems, statistical physics on the random lattice, random matrix theory, topological string theory,... All these topics share certain relations, called "loop equations" or…

Let $d\in\mathbb{Z}$ and $p_i$ be an integral polynomial with $p_i(0)=0,1\leq i\leq d$. It is shown that if $S$ is thickly syndetic in $\mathbb{Z}$, then $\{(m,n)\in\mathbb{Z}^2:m+p_i(n),m+p_2(n),\ldots,m+p_d(n)\in S\}$ is thickly syndetic…

For a dynamical system, we study the set of points $\cal W$ whose orbit approximates any chosen point at certain specified rates. Our basic setting is that of left shift acting on topological Markov chains endowed with a local weak Gibbs…

Takens' Embedding Theorem remarkably established that concatenating M previous outputs of a dynamical system into a vector (called a delay coordinate map) can be a one-to-one mapping of a low-dimensional attractor from the system state…

Non-convex methods for linear inverse problems with low-dimensional models have emerged as an alternative to convex techniques. We propose a theoretical framework where both finite dimensional and infinite dimensional linear inverse…