Related papers: Friezes, weak friezes, and T-paths

The structural properties of packed soft-core particles provide a platform to understand the cross-pollinated physical concepts in solid-state- and soft-matter physics. Confined on spherical surface, the traditional differential geometry…

This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We…

Fusion frames enable signal decompositions into weighted linear subspace components. For positive integers p, we introduce p-fusion frames, a sharpening of the notion of fusion frames. Tight p-fusion frames are closely related to the…

A new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy topological space is introduced and it is established that this class of fuzzy closed sets lies between fuzzy closed sets and fuzzy generalized closed sets.…

One of the most interesting phenomena in the soft-matter realm consists in the spontaneous formation of super-molecular structures (microphases) in condition of thermodynamic equilibrium. A simple mechanism responsible for this…

It is conjectured that all decomposable (i.e. interior can be triangulated without adding new vertices) polyhedra with vertices in convex position are infinitesimally rigid and only recently has it been shown that this is indeed true under…

We introduce the notion of weakly associative algebra and its relations with the notion of nonassociative Poisson algebras.

We ask when a finite set of t-structures in a triangulated category can be `averaged' into one t-structure or, equivalently, when the extension closure of a finite set of aisles is again an aisle. There is a straightforward, positive answer…

A rectangulation is a decomposition of a rectangle into finitely many rectangles. Via natural equivalence relations, rectangulations can be seen as combinatorial objects with a rich structure, with links to lattice congruences, flip graphs,…

This article develops the theory of fusion categories acting on algebras. We will demonstrate that weak Hopf algebra actions on algebras correspond to specific actions of fusion categories. As an application of this theory, we introduce a…

We introduce a framework for Riemannian diffeology. To this end, we use the tangent functor in the sense of Blohmann and one of the options of a metric on a diffeological space in the sense of Iglesias-Zemmour. As a consequence, the…

In this paper we use the connections between tropical algebraic geometry and rigid analytic geometry in order to prove two main results. We use tropical methods to prove a theorem about the Newton polygon for convergent power series in…

The t-J_z model is the strongly anisotropic limit of the t-J model which captures some general properties of the doped antiferromagnets (AF). The absence of spin fluctuations simplifies the analytical treatment of hole motion in an AF…

The aim of this paper is to develop the combinatorics of constructions associated to what we call \emph{triangular partitions}. As introduced in arXiv:2102.07931, these are the partitions whose cells are those lying below the line joining…

Theory of weak localization is developed for two-dimensional holes in the presence of in-plane magnetic field. The Zeeman splitting even in the hole momentum results in the spin-dependent phase changing the quantum interference. The…

We perform a novel analysis of the granular texture of a granular bed close to stability limit. Our analysis is based on a unique criterion of friction mobilisation in a simulated two-dimensional packing. In this way, we recover the bimodal…

We review some recent results on properties of tensor product and fusion coefficients under complex conjugation of one of the factors. Some of these results have been proven, some others are conjectures awaiting a proof, one of them…

We consider and discretize a mixed formulation for linear elasticity with weakly imposed symmetry in two and three dimensions. Whereas existing methods mainly deal with simplicial or polygonal meshes, we take advantage of isogeometric…

Fine-grained complexity theory is the area of theoretical computer science that proves conditional lower bounds based on the Strong Exponential Time Hypothesis and similar conjectures. This area has been thriving in the last decade, leading…

Pattern formation in parametric surface waves is studied in the limit of weak viscous dissipation. A set of quasi-potential equations (QPEs) is introduced that admits a closed representation in terms of surface variables alone. A multiscale…