In this paper, within the constructive algebraic analysis approach to linear systems, we study classical linear systems of partial differential (PD) equations in two or three independent variables with constant coefficients appearing in mathematical physics and engineering sciences such as the Stokes and Oseen equations studied in hydrodynamics. We first provide a precise algebraic description ...

Difference-differential Gröbner bases and the algorithms were introduced by M.Zhou and F.Winkler (2006). In this paper we will make further investigations for the key concept of S-polynomials in the algorithm and we will improve technically the algorithm. Then we apply the algorithm to compute the differencedifferential dimension polynomial of a difference-differential module and of a system of...

A ghost in the stable module category of a group G is a map between representations of G that is invisible to Tate cohomology. We show that the only non-trivial finite p-groups whose stable module categories have no non-trivial ghosts are the cyclic groups C2 and C3. We compare this to the situation in the derived category of a commutative ring. We also determine for which groups G the second p...

in this paper we study the module contractibility ofbanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. also weinvestigate module contractibility of banach algebras with theconcept of the module diagonal.

Abstract. We show that for any prime number l > 2 the minus class group of the field of the l-th roots of unity Qp(ζl) admits a finite free resolution of length 1 as a module over the ring Ẑ[G]/(1 + ι). Here ι denotes complex conjugation in G = Gal(Qp(ζl)/Qp) ∼= (Z/lZ)∗. Moreover, for the primes l ≤ 509 we show that the minus class group is cyclic as a module over this ring. For these primes we...

Abstract. In this paper we study the groups of circular numbers and circular units in Sinnott’s sense in real abelian fields with exactly four ramified primes under certain conditions. More specifically, we construct Z-bases for them in five special infinite families of cases. We also derive some results about the corresponding module of relations (in one family of cases, we show that the modul...

A novel iterative algorithm is proposed to compute the theoretical minimum initiation interval of a given recurrent algorithm when there is a known, fixed inter-module communication delay. Specifically, for a twin-module implementation problem, a novel representation called necessary initiation interval is introduced to faciliate the development of an iterative algorithm which yields both the m...

4. Describe the D-module extD(M,D) in terms of generators and relations. 5. Prove that extD(M,D) is a 1-dimensional Q(a, k, ω, ζ)-vector space. Give a basis ρ(Λ) of extD(M,D), where ρ : D 3 −→ D3/(RD4) denotes the canonical projection. 6. Deduce that ρ(Λ) generates extD(M,D), i.e., ext 1 D(M,D) is a cyclic D-module. 7. Consider the matrix P = (R − Λ) ∈ D3×5. Show that P admits a left-inverse ov...