We study the Adjusted Winner procedure of Brams and Taylor for dividing goods fairly between two individuals, and prove several results. In particular we show rigorously that as the differences between the two individuals become more acute they both benefit. We introduce a geometric approach which allows us to give alternate proofs of some of the Brams-Taylor results and which gives some hope f...

Let K denote a field and let V denote a vector space over K with finite positive dimension. We consider a pair of K-linear transformations A : V → V and A : V → V that satisfy the following conditions: (i) each of A,A is diagonalizable; (ii) there exists an ordering {Vi} d i=0 of the eigenspaces of A such that A Vi ⊆ Vi−1+Vi+Vi+1 for 0 ≤ i ≤ d, where V−1 = 0 and Vd+1 = 0; (iii) there exists an ...

We say that a C*-algebra A has the ‘sublattice property’ if the set P(A) of all projections in A is a sublattice of the projection lattice of its enveloping von Neumann algebra A∗∗. It is shown that this property is equivalent to the requirement that all pairs of projections have strictly positive ‘angle’. We discuss this property in relation to some results obtained by C. Akemann and by A. Laz...

Citation: Sommer S, Clemens D, Yücel M, Pfannkuche O, Hall POJ, Almroth-Rosell E, Schulz-Vogt HN and Dale AW (2017) Major Bottom Water Ventilation Events Do Not Significantly Reduce Basin-Wide Benthic N and P Release in the Eastern Gotland Basin (Baltic Sea). Front. Mar. Sci. 4:18. doi: 10.3389/fmars.2017.00018 Major Bottom Water Ventilation Events Do Not Significantly Reduce Basin-Wide Benthic...

Let K denote a field and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A∗ : V → V that satisfy (i)–(iv) below: (i) Each of A, A∗ is diagonalizable. (ii) There exists an ordering V0, V1, . . . , Vd of the eigenspaces of A such that A ∗Vi ⊆ Vi−1 + Vi + Vi+1 for 0 ≤ i ≤ d, where V−1 = 0, Vd+1 = 0. (iii) There exists an...

It is well known, see [D. Carlson, T. Markham, Schur complements of diagonally dominant matrices, Czech. Math. Schur complement of a strictly diagonally dominant matrix is strictly diagonally dominant , as well as its diagonal-Schur complement. Also, if a matrix is an H-matrix, then its Schur complement and diagonal-Schur complement are H-matrices, too, see [J. Liu, Y. Huang, Some properties on...

in this study a nonlinear asymmetric instability analysis carried out to study primary atomization of annular liquid sheets emanating from the prefilming airblast atomizer using a perturbation method and potential flow assumption. in this direction, firstly governing equations derived according to potential flow assumption and conservation equations while dynamic and static boundary condition a...