In Multi-Criteria Decision Analysis, the well-known weighted sum method for aggregating normalised relative priorities ignores the unit of scale that may vary across the criteria and thus causes rank reversals. A new aggregation rule that explicitly includes the norms of priority vectors is derived and shown as a remedy for it. An algorithmic procedure is presented to demonstrate how it can as ...

We study the symplectic geometry of moduli spaces M r of polygons with xed side lengths in Euclidean space. We show that M r has a natural structure of a complex analytic space and is complex-analytically isomorphic to the weighted quotient of (S 2) n constructed by Deligne and Mostow. We study the Hamiltonian ows on M r obtained by bending the polygon along diagonals and show the group generat...

The Dirichlet space D is the space of all analytic functions f on the open unit disc D such that f ′ is square integrable with respect to two-dimensional Lebesgue measure. In this paper we prove that the invariant subspaces of the Dirichlet shift are in 1-1 correspondence with the kernels of the Dirichlet-Hankel operators. We then apply this result to obtain information about the invariant subs...

We extend the notion of L2 B discrepancy provided in [E. Novak, H. Woźniakowski, L2 discrepancy and multivariate integration, in: Analytic number theory. Essays in honour of Klaus Roth. W. W. L. Chen, W. T. Gowers, H. Halberstam, W. M. Schmidt, and R. C. Vaughan (Eds.), Cambridge University Press, Cambridge, 2009, 359 – 388] to the weighted L2 B discrepancy. This newly defined notion allows to ...

We develop a theory of removable singularities for the weighted Bergman space Aμ(Ω) = {f analytic in Ω : R Ω |f | dμ < ∞}, where μ is a Radon measure on C. The set A is weakly removable for Aμ(Ω \ A) if Aμ(Ω \ A) ⊂ Hol(Ω), and strongly removable for Aμ(Ω \A) if Aμ(Ω \A) = Aμ(Ω). The general theory developed is in many ways similar to the theory of removable singularities for Hardy H spaces, BMO...