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We define higher semiadditive algebraic K-theory, a variant of algebraic K-theory that takes into account higher semiadditive structure, as enjoyed for example by the $K(n)$- and $T(n)$-local categories. We prove that it satisfies a form of…
We establish sharp (or `refined') comparison theorems for the Klein--Gordon equation. We show that the condition $V_a\le V_b$, which leads to $E_a\le E_b$, can be replaced by the weaker assumption $U_a\le U_b$ which still implies the…
Stochastic symmetries and related invariance properties of finite dimensional SDEs driven by general cadlag semimartingales taking values in Lie groups are defined and investigated. The considered set of SDEs, first introduced by S. Cohen,…
Superradiance is one of the outstanding problems in quantum optics since Dicke introduced the concept of enhanced directional spontaneous emission by an ensemble of identical two-level atoms. The effect is based on correlated collective…
A rigorous \textit{ab initio} derivation of the (square of) Dirac's equation for a single particle with spin is presented. The general Hamilton-Jacobi equation for the particle expressed in terms of a background Weyl's conformal geometry is…
We consider substitutions on compact alphabets and provide sufficient conditions for the diffraction to be pure point, absolutely continuous and singular continuous. This allows one to construct examples for which the Koopman operator on…
This paper extends our previous works arXiv:1802.07306 [math.NT], arXiv:1808.02382 [math.NT] on determining the spectrum, in the Berkovich sense, of ultrametric linear differential equations. Our previous works focused on equations with…
In this current work, we revisit the recent improvement of the discrete Hardy's inequality in one dimension and establish an extended improved discrete Hardy's inequality with its optimality. We also study one-dimensional discrete Copson's…
An important question in dynamical systems is the classification problem, i.e., the ability to distinguish between two isomorphic systems. In this work, we study the topological factors between a family of multidimensional substitutive…
A new class of sign-symmetric matrices is introduced in this paper. Such matrices are named J--sign-symmetric. The spectrum of a J--sign-symmetric irreducible matrix is studied under assumptions that its second compound matrix is also…
A particularly important substructure in modeling joint linear chance-constrained programs with random right-hand sides and finite sample space is the intersection of mixing sets with common binary variables (and possibly a knapsack…
We consider discrete-time switching systems composed of a finite family of affine sub-dynamics. First, we recall existing results and present further analysis on the stability problem, the existence and characterization of compact…
The optical interference constitutes a paramount resource in modern physics. At the scale of individual atoms and photons, it is a diverse concept that causes different coherent phenomena. We present the experimental characterization of…
We investigate the increasingly prominent task of jointly inferring multiple networks from nodal observations. While most joint inference methods assume that observations are available at all nodes, we consider the realistic and more…
In this paper, we study the descriptive set theoretic complexity of the equivalence relation of conjugacy of Toeplitz subshifts of a residually finite group $G$. On the one hand, we show that if $G = \mathbb{Z}$, then topological conjugacy…
The admittance of two types of Josephson weak links is calculated, i.e., of a one-dimensional superconducting wire with a local suppression of the order parameter, and the second is a short S-c-S structure, where S denotes a superconductor…
The aim of this article is to obtain a better understanding and classification of strictly ergodic topological dynamical systems with discrete spectrum. To that end, we first determine when an isomorphic maximal equicontinuous factor map of…
We study the mathematical aspects of the Bose Einstein Condensation for the pure hopping model describing arrays of Josephson junctions on non homogeneous networks. The graphs under investigation are obtained by adding density zero…
The celebrated Takens' embedding theorem concerns embedding an attractor of a dynamical system in a Euclidean space of appropriate dimension through a generic delay-observation map. The embedding also establishes a topological conjugacy. In…
Various threshold effects are investigated on a discrete quasi-1D scattering system. In particular, one of these effects is to add corrections to Levinson's theorem. We explain how these corrections are due to the opening or to the closing…