Mathematics

In the generality of a rigidly-compactly generated tensor triangulated category, we introduce semi-Bousfield classes in terms of the vanishing of the tensor product in positive degrees with respect to a fixed reasonable $t$-structure. We…

In this paper, we answer negatively to a question posed in the context of the 2025 Oberwolfach Mini-Workshop ``The Yang-Baxter Equation and Representations of Braid Groups'' regarding the existence of split extensions classifiers in the…

This paper gives a structural explanation for the Z-relation by modelling pitch-class sets as complete weighted graphs and encoding their interval content in a composition of $n$ via an additivity rule. We introduce the realization number…

This article explores several fundamental aspects of fuzzy $\mathscr{F}$-metric spaces and their applications in mathematical analysis. We investigate some essential properties concerning compactness and total boundedness in fuzzy…

This article is a generalization of a result in Quillen's note ``Module theory over non-unital rings'' giving a one-to-one correspondence between bilocalization of abelian categories of modules and idempotent ideals of the base ring.…

In this article, it is proved that the non-trivial zeros of the Riemann zeta function must lie on the critical line, known as the Riemann hypothesis.

K. S. S. Nambooripad introduced an interesting class of categories known as normal categories, which are categories with subobjects, morphisms admitting factorization and having sufficiently many cones. These normal categories plays…

We develop a unified analytical and dynamical framework for the qualitative study of the one-parameter family of generalized Dirichlet eta functions $\eta_{a}(t)=\sum_{m\ge0}(-1)^{m}(am+1)^{-t}$, $a>0$, $t>0$, which includes the classical…

We establish the equivalence between models of enhanced $2$-sketches and algebras over monads, including the (co)lax morphisms. More precisely, for any enhanced limit $2$-sketch $\mathbb{T}$ with tight cones, the enhanced $2$-category…

In this article we solve the Cauchy problem for the relaxation equation posed in a framework of variable order fractional calculus. After introducing some general mathematical theory we establish concepts of Scarpi derivative and transition…

We investigate a new notion of regularity for tensor triangulated categories, called residual regularity. We show that residual regularity descends and ascends via finite separable extensions and we classify all finite groups whose derived…

Drawing on well-known results from the theory of canonical extensions and the theory of categories enriched over a quantale, we define canonical extensions of quantale-enriched categories and establish their basic properties.

Lezama \cite{LezamaLatorre2017} introduced the notion of semi-graded ring with the aim of generalizing $\mathbb{Z}$-graded rings and several families of noncommutative rings of polynomial type non-$\mathbb{N}$-graded such as the skew…

The graph Fourier transform (GFT) is a fundamental tool in graph signal processing and has recently been extended to the graph fractional Fourier transform (GFRFT). Existing sampling methods in the GFRFT domain are primarily designed to…

For $p,q\in\mathbb{N}$ and $\alpha,\beta\in\mathbb{R}$, we investigate the family of improper integrals \[\int_0^\infty\frac{(\cos\alpha x-\cos\beta x)^p}{x^q}dx.\] We establish a complete classification of the parameter ranges $(p, q;…

This is an incomplete attempt to show that the upper bound of $\lesssim n^\frac{4}{3}$ on the number unit distances determined by a large finite set of $n$ points in the plane is not sharp. The methods also say something about sets of $n$…

We study equivariant perfect matchings on the Boolean hypercube $\B^6$ under the Klein four-group $K_4 = \langle \comp, \rev \rangle$ generated by bitwise complement and reversal. Among matchings using only $\comp$ or $\rev$ pairings, there…

In the philosophical tradition of `analytic pragmatism', which attempts to account for linguistic meanings in terms of their practices of use, logical expressivism is a theory which offers a distinct perspective on logic. We shed light on…

A limit of a (small) diagram $d : J \to E$ in a complete category $E$ can be thought of as specifying a set of equations involving the objects of $E$. To motivate this intuitively, one can think of each object $d(j)$ as a "variable" and…

This note studies a concrete bitwise and triangular coordinate model for the central product of n copies of the quaternion group Q8. The positive basis elements are words of length n in the alphabet {1, 2, 4, 7}, identified with i, j, k,…