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We study the connectedness locus $\mathcal{N}$ for the family of iterated function systems of pairs of homogeneous affine-linear maps in the plane. We prove this set is regular closed (i.e., it is the closure of its interior) away from the…
The model of local electron pairs and itinerant fermions coupled via charge exchange mechanism, which mutually induces superconductivity in both subsystems is studied for anisotropic pairing symmetry. The phase diagram is presented and the…
Inspired by code vertex operator algebras (VOAs) and their representation theory, we define code algebras, a new class of commutative non-associative algebras constructed from binary linear codes. Let $C$ be a binary linear code of length…
Sellami and Sirvent conjectured that the balanced pair algorithm fails for the following pair of Pisot substitutions: \[ \varphi_0: \begin{array}{l} a \mapsto abc b \mapsto a c \mapsto ac \end{array} \quad \text{ and } \quad \varphi_1:…
Let $A \subseteq E$ be a given extension of Hopf (respectively Lie) algebras. We answer the \emph{classifying complements problem} (CCP) which consists of describing and classifying all complements of $A$ in $E$. If $H$ is a given…
For a given graph whose edges are labeled with general real numbers, we consider the set of functions from the vertex set into the Euclidean plane such that the distance between the images of neighbouring vertices is equal to the…
The hamiltonian of the $N$-state superintegrable chiral Potts (SICP) model is written in terms of a coupled algebra defined by $N-1$ types of Temperley-Lieb generators. This generalises a previous result for $N=3$ obtained by J. F. Fjelstad…
In this paper, we investigate the structure and properties of additive complementary dual (ACD) codes over the mixed alphabet $\mathbb{F}_2\mathbb{F}_4$ relative to a certain inner product defined over $\mathbb{F}_2\mathbb{F}_4$. We…
Ehrenborg noted that all tilings of a bipartite planar graph are encoded by its cubical matching complex and claimed that this complex is collapsible. We point out to an oversight in his proof and explain why these complexes can be the…
A \emph{Fibonacci cordial labeling} of a graph \( G \) is an injective function \( f: V(G) \rightarrow \{F_0, F_1, \dots, F_n\} \), where \( F_i \) denotes the \( i^{\text{th}} \) Fibonacci number, such that the induced edge labeling \(…
In this paper a class of linear maps on the 2-torus and some planar piecewise isometries are discussed. For these discontinuous maps, by introducing codings underlying the map operations, symbolic descriptions of the dynamics and…
Since the discovery of unconventional superconductivity in cuprates, unraveling the pairing mechanism of charge carriers in doped antiferromagnets has been a long-standing challenge. Motivated by the discovery of high-T$_c$…
Constrained clustering integrates domain knowledge through pairwise constraints. However, existing deep constrained clustering (DCC) methods are either limited by anchors inherent in end-to-end modeling or struggle with learning…
Recently some mixed alphabet rings are involved in constructing few-Lee weight additive codes with optimal or minimal Gray images using suitable defining sets or down-sets. Inspired by these works, we choose the mixed alphabet ring…
The Lefschetz hyperplane section theorem asserts that an affine variety is homotopy equivalent to a space obtained from its generic hyperplane section by attaching some cells. The purpose of this paper is to describe attaching maps of these…
We prove the minimality of the CW-complex structure for complements of hyperplane arrangements in $\mathbb C^n$ by using the theory of Lefschetz pencils and results on the variation maps within a pencil of hyperplanes. This also provides a…
Consider the additive Gaussian model $Y = X + \sigma Z$, where $X \sim P$ is an unknown signal, $Z \sim N(0,1)$ is independent of $X$, and $\sigma > 0$ is known. Let $Q$ denote the law of $Y$. We construct a hierarchy of denoisers $T_0,…
We develop a version of Cichon's diagram for cardinal invariants on the generalized Cantor space 2^kappa or the generalized Baire space kappa^kappa where kappa is an uncountable regular cardinal. For strongly inaccessible kappa, many of the…
We show that the problem of classifying, up to isomorphism, the collection of zero-entropy mixing automorphisms of a standard non-atomic probability space, is intractible. More precisely, the collection of isomorphic pairs of automorphisms…
In this paper, we study the non-singular extension problem of horizontal stable fold maps. This problem asks what conditions ensure the existence of a submersion whose restriction to the boundary coincides with a given map, called a…