Algebraic structures and state theory represent a confluence of abstract algebra and logic, where the former provides a rigorous framework for describing systems such as BL-algebras, residuated ...

Algebraic structures, ranging from groups and rings to modules and fields, constitute the foundation of modern mathematics. Among these, Hopf algebras have emerged as pivotal constructions that ...

This is a preview. Log in through your library . Abstract Let X be a finite, n-dimensional, r-connected CW complex. We prove the following theorem: If p ≥ n/r is an odd prime, then the loop space ...

If you’ve ever taken an algebra or physics class, then you’ve met a parabola, the simple curve that can model how a ball flies through the air. The most important part of a parabola is the vertex — ...

How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of recent work by the ...

Let à denote a smooth compactification of the k-fold fiber product of the universal family A1 → M of elliptic curves with level N structure. The purpose of this paper is to completely describe the ...

Harvard Mathematics professor Lauren K. Williams has been awarded a 2025 MacArthur Fellowship for her groundbreaking research ...

In a collaboration led by EPFL’s Blue Brain, scientists discover patterns of brain activity – never before observed – with the help of mathematics, providing insight into how neurons collectively ...