There is a close relation between comprehensive Gröbner bases and non-parametric Gröbner bases over commutative von Neumann regular rings. By this relation, Gröbner bases over a commutative von Neumann regular ring can be viewed as an alternative to comprehensive Gröbner bases. (Therefore, this Gröbner basis is called an “alternative comprehensive Gröbner basis (ACGB)”.) In the first part of th...

Gröbner bases in polynomial rings have numerous applications in geometry, applied mathematics, and engineering. We show a few applications of Gröbner bases in robotics, formulated in the language of Clifford algebras, and in engineering to the theory of curves, including Fermat and Bézier cubics, and interpolation functions used in finite element theory.

Transitional justice is guided by three main theories of justice: retributive, restorative, and reparative. Currently, the theories are predominantly perceived as mutually exclusive rather than mutually reinforcing. This paper seeks to reconceptualize the way scholars and practitioners comprehend and use the theories by looking at the goals and the unique focus of each theory. Through this anal...

Overview These notes consists of ve lectures. Each lecture covers the material that I will present with fuller details and exercises. I have also included some material in appendices which the reader might nd interesting but which I will not have time to cover in my lectures. Lecture 1 introduces both linear Grr obner bases and Grr obner bases for algebras. Lecture 2 surveys some of the basis a...

An uncovering-by-bases for a group G acting on a finite set Ω is a set U of bases forG such that any r-subset of Ω is disjoint from at least one base in U, where r is a parameter dependent on G. They have applications in the decoding of permutation groups when used as error-correcting codes, and are closely related to covering designs. We give constructions for uncoverings-by-bases for many fam...