This paper focuses on the geometric theory of scroll compressor, which includes the determination of the discharge angle, the calculation of the volume in different compression stages, the axial gas force under the condition that the number of scroll turns equals an arbitrary real number. NOMENCLATURE . (J :expanding angle of the involute (rad) a :initial angle of the involute (rad) 6 : orbitin...

We analyze the algebraic structures of G–Frobenius algebras which are the algebras associated to global group quotient objects. Here G is any finite group. These algebras turn out to be modules over the Drinfeld double of the group ring k[G]. We furthermore prove that discrete torsion is a universal group action of H(G, k∗) on G–Frobenius algebras by isomorphisms of the underlying linear struct...

Torsion objects of von Neumann categories describe the phenomenon ”spectrum near zero” discovered by S. Novikov and M. Shubin. In this paper we classify Hermitian forms on torsion objects of a finite von Neumann category. We prove that any such Hermitian form can be represented as the discriminant form of a degenerate Hermitian form on a projective module. We also find the relation between the ...

In this article, we formalize the definition of divisible Z-module and its properties in the Mizar system [3]. We formally prove that any non-trivial divisible Z-modules are not finitely-generated. We introduce a divisible Z-module, equivalent to a vector space of a torsion-free Z-module with a coefficient ring Q. Z-modules are important for lattice problems, LLL (Lenstra, Lenstra and Lovász) b...

in this paper‎, ‎we introduce the notion of $(m,n)$-‎algebr‎aically compact modules as an analogue of algebraically‎ ‎compact modules and then we show that $(m,n)$-algebraically‎ ‎compactness‎ ‎and $(m,n)$-pure injectivity for modules coincide‎. ‎moreover‎, ‎further characterizations of a‎ ‎$(m,n)$-pure injective module over a commutative ring are given‎.