Unlike the (classical) Kolakoski sequence on the alphabet {1, 2}, its analogue on {1, 3} can be related to a primitive substitution rule. Using this connection, we prove that the corresponding bi-infinite fixed point is a regular generic model set and thus has a pure point diffraction spectrum. The Kolakoski-(3, 1) sequence is then obtained as a deformation, without losing the pure point diffra...

Unlike the (classical) Kolakoski sequence on the alphabet {1, 2}, its analogue on {1, 3} can be related to a primitive substitution rule. Using this connection, we prove that the corresponding bi-infinite fixed point is a regular generic model set and thus has a pure point diffraction spectrum. The Kolakoski-(3, 1) sequence is then obtained as a deformation, without losing the pure point diffra...

‎given a finite non-cyclic group $g$‎, ‎call $sigma(g)$ the smallest number of proper subgroups of $g$ needed to cover $g$‎. ‎lucchini and detomi conjectured that if a nonabelian group $g$ is such that $sigma(g) < sigma(g/n)$ for every non-trivial normal subgroup $n$ of $g$ then $g$ is textit{monolithic}‎, ‎meaning that it admits a unique minimal normal subgroup‎. ‎in this paper we show how thi...

In this article, we investigate symmetric $(v,k,\lambda)$ designs $\mathcal{D}$ with $\lambda$ prime admitting flag-transitive and point-primitive automorphism groups $G$. We prove that if $G$ is an almost simple group socle a finite of Lie type, then either the point-hyperplane design projective space $\mathrm{PG}_{n-1}(q)$, or it parameters $(7,4,2)$, $(11,5,2)$, $(11,6,3)$ $(45,12,3)$.

‎A universal schema for diagonalization was popularized by N.S‎. ‎Yanofsky (2003)‎, ‎based on a pioneering work of F.W‎. ‎Lawvere (1969)‎, ‎in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function‎. ‎It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema‎. ‎Here‎, ‎we fi...

We prove that a primitive substitution Delone set, which is pure point diffractive, is a Meyer set. This answers a question of J. C. Lagarias. We also show that for primitive substitution Delone sets, being a Meyer set is equivalent to having a relatively dense set of Bragg peaks. The proof is based on tiling dynamical systems and the connection between the diffraction and dynamical spectra.

We consider the dynamical system created by iterating a morphism of a projective variety over the field of fractions of a discrete valuation ring. In the case of good reduction, we study the primitive period of a periodic point on the residue field. We start by defining good reduction, examine the behavior of primitive periods under good reduction, and end with an application to programmaticall...

We introduce a novel template-based modeling technique for 3D point clouds sampled from unknown buildings. The approach is based on a hierarchy algebraic template to fit noisy point clouds with sharp features. In the hierarchy template, the first-level, i.e., the lowest-level, contains three kinds of primitive geometries: plane, sphere, and cylinder. These primitive geometries are represented i...

We prove that a primitive substitution Delone set, which is pure point diffractive, is a Meyer set. This answers a question of J. C. Lagarias. We also show that for primitive substitution Delone sets, being a Meyer set is equivalent to having a relatively dense set of Bragg peaks. The proof is based on tiling dynamical systems and the connection between the diffraction and dynamical spectra.

t=1 γ (P 1P o2 . . . P o)t (Y |x) for all Y ⊆ X and x ∈ X. We will assume throughout this supplementary material that when we refer to an optimal policy π∗, it is a policy over primitive actions. Because we have assume that O contains the set of primitive actions A, the fixed point of the SMDP Bellman operator T and the MDP Bellman operator T is the optimal value function V ∗. Thus Tπ is equiva...