In [6], we defined q-analogues of alien derivations and stated their basic properties. In this paper, we prove the density theorem and the freeness theorem announced in loc. cit..

We introduce the concept of presentation for the Archimedean components of finitely generated commutative monoids. Some properties like being cancellative, torsion freeness and separativity are studied under this new point of view.

1 Institute of Mathematics and Computer Science Academy of Sciences of Moldova Academiei 5, Chişinău, MD-2028, Moldova [email protected] 2 Key Laboratory of Image Information Processing and Intelligent Control of Education Ministry of China, School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China 3 Faculty of Informatics, TU Wien Favoritenstraße 9–11, 1040 Vienna, ...

Abstract We use tools from free probability to study the spectra of Hermitian operators on infinite graphs. Special attention is devoted universal covering trees finite For these graphs, we derive a new variational formula for spectral radius and provide proofs results due Sunada Aomoto using probability. With goal extending applicability techniques beyond trees, introduce combinatorial product...

We show that deciding square-freeness of a sparse univariate polynomial over ZZ and over the algebraic closure of a nite eld IFq of p elements is NP-hard. We also discuss some related open problems about sparse polynomials.