Related papers: Countable homogeneous Steiner triple systems avoid…
The N-dimensional generalization of Bertrand spaces as families of Maximally superintegrable systems on spaces with nonconstant curvature is analyzed. Considering the classification of two dimensional radial systems admitting 3 constants of…
In this paper, we introduce the concept of Arf special gaps of an Arf numerical semigroup, and an algorithm for computing all Arf special gaps of a given Arf numerical semigroup. We introduce the concept of Arf-irreducible numerical…
In this paper we show that for a given 3-manifold and a given Heegaard splitting there are finitely many preferred decomposing systems of $3g - 3$ disjoint essential disks. These are characterized by a combinatorial criterion which is a…
We prove several structural properties of Steiner triple systems (STS) of order 3w+3 that include one or more transversal subdesigns TD(3,w). Using an exhaustive search, we find that there are 2004720 isomorphism classes of STS(21)…
In [11] Sklinos proved that any uncountable free group is not $\aleph_1$-homogenenous. This was later generalized by Belegradek in [1] to torsion-free residually finite relatively free groups, leaving open whether the assumption of residual…
Building on the work of Avraham, Rubin, and Shelah, we aim to build a variant of the Fra\"iss\'e theory for uncountable models built from finite submodels. With this aim, we generalize the notion of an increasing set of reals to other…
Definable stationary sets, and specifically, ordinal definable ones, play a significant role in the study of canonical inner models of set theory and the class HOD of hereditarily ordinal definable sets. Fixing a certain notion of…
We produce a variety of odd bounded Fredholm modules and odd spectral triples on Cuntz-Krieger algebras by means of realizing these algebras as "the algebra of functions on a non-commutative space" coming from a sub shift of finite type. We…
Generalizing Krieger's finite generation theorem, we give conditions for an ergodic system to be generated by a pair of partitions, each required to be measurable with respect to a given sub-algebra, and also required to have a fixed size.
We introduce the notion of a restricted exchangeable partition of $\mathbb{N}$. We obtain integral representations, consider associated fragmentations, embeddings into continuum random trees and convergence to such limit trees. In…
Modern experimental methods enable the creation of self-assembly building blocks with tunable interactions, but optimally exploiting this tunability for the self-assembly of desired structures remains an important challenge. Many studies of…
A new infinite family of examples of finite non-bicolorable configurations of rays in Hilbert space is described. Such configurations appear in the analysis of quantum mechanics in terms of Bell's inequalities and Kochen-Specker theorem and…
We extend a distributed finite element method built upon model order reduction to arbitrary polynomial degree using a hybrid Nitsche scheme. The new method considerably simplifies the transformation of the finite element system to the…
For certain Lie algebras g, we can use a Z/5Z-grading and define a quartic form and a skew-symmetric bilinear form on the degree 1 component, g_1, thereby constructing a Freudenthal triple system. The structure of the Freudenthal triple…
The Kochen-Specker theorem states that a 3-dimensional complex Euclidean space admits a finite configuration of projective lines such that the corresponding quantum observables (the orthogonal projectors) cannot be assigned with 0 and 1…
The purpose of this paper is to contribute to the theory of profinite semigroups by considering the special class consisting of those all of whose finitely generated closed subsemigroups are countable, which are said to be locally…
We show that a large class of non-degenerate second-order (maximally) superintegrable systems gives rise to Hessian structures, which admit natural (Hessian) coordinates adapted to the superintegrable system. In particular, abundant…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…
We sow that there exists a generic extension of the G\"{o}del's constructible universe in which diamond holds and there exists a subset $Y \subseteq \omega_1$ such that for stationary many $\delta < \omega_1,$ the set $Y \cap \delta$ is not…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…