Piotr Krasoń

In our recent paper, “Algorithms for Determination of t-Module Structures on Some Extension Groups,” published in International Journal of Number Theory, Vol. 21, No. 8 (2025) 1889–1922, we identified a gap in Algorithm 2 that affects Example 4.2. In this corrigendum, we describe the nature of this issue and present a corrected version of the algorithm.

We introduce and study a natural class of Anderson t- modules, called triangular t-modules, characterized by having Drinfeld modules as their $τ$-composition factors. They form a homologically meaningful generalization of Drinfeld modules and exhibit rich arithmetic structure.\smallskip We establish criteria for purity, strict and almost strict, and develop a reduction procedure that lowers the degrees of the defining biderivations. As a consequence, every almost strictly pure triangular t-module becomes strictly pure after a finite base extension. We then investigate morphisms and isogenies between triangular t-modules, provide a characterization of triangular isogenies, and describe the algebra of endomorphisms, including a criterion for commutativity. On the analytic side, we show that all triangular t- modules are uniformizable and establish finiteness and purity criteria with consequences for Taelman's conjecture. Finally, we develop a duality theory for triangular t- modules and their biderivations, proving compatibility with $τ$-composition series and establishing analogues of the Cartier-Nishi theorem and the Weil-Barsotti formula.

In their recent work the second and the third authors extended the methods of M. A. Papanikolas and N. Ramachandran and determined the t-module structure on [ ] where [ ] and [ ] were Anderson t-modules over [ ] of some specific types. This approach involved the concept of biderivation and certain reduction algorithm. In this paper, we generalize these results and present a complete algorithm for computation of t-module structure on [ ] for t-modules [ ] and [ ] such that [ ] The last condition is not sufficient for our algorithm to be executable. We show that it can be applied when the matrix at the biggest power of [ ] in [ ] is invertible. We also introduce a notion of [ ]-composition series which we find suitable for the additive category of t-modules and show that under certain assumptions on the composition series of [ ] and [ ] our algorithm is also executable.

We consider the relative motion of the system of two masses connected by a spring. We analyze it in a range of the Hooke’s law and show that the equations of the relative motion of the system are nonlinear once the equilibrium length of the spring is nonzero. Although the way of deriving the equations of motion is standard in classical mechanics solving them is a complicated and interesting problem of mathematical physics. The analysis leads naturally to elliptic integrals. We obtain complete formulas in an interesting, from both mathematical and physical point of view, way. Our analysis might be useful in some problems of molecular dynamics of diatomic molecules.

In this paper we compute in some new cases the cardinalities of the fibers of certain natural fibrations that appear in the analysis of the configuration space of the Heisenberg ring. This is done by means of certain cyclic group actions on some subsets o