Abstract We study direct-sum decompositions of torsion-free, finitely generated modules over a (commutative) Bass ring R through the factorization theory corresponding monoid T ( ). Results Levy–Wiegand and Levy–Odenthal together with local case yield an explicit description The is typically neither factorial nor cancellative. Nevertheless, we construct transfer homomorphism to graph agglomerat...

This paper estimates the risks of financial distress in UK universities, and uses these estimates to examine the basis of the annual levies paid to the UK’s Pension Protection Fund by the Universities Superannuation Scheme, a multi-employer scheme covering 391 universities and related institutions. The paper compares the payments between the two alternative participating arrangements for multi-...

An approximate solution to the time-dependent density-functional theory response equations for finite systems is developed, yielding corrections to the single-pole approximation. These explain why allowed Kohn-Sham transition frequencies and oscillator strengths are usually good approximations to the true values, and why sometimes they are not. The approximation yields simple expressions for Gö...

Local government units carry costs related to the shaping and spatial development of communes, are consequently interested in sharing benefits that land property owners gain on this account. This is possible through, inter alia, betterment levy. The aim study was determine reasons for discontinuation levy charging Poland, illustrated with example Gorlicki County. A further classify suggest dire...