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.

We prove that when the number of (potential) buyers is at least three, every ex post equilibrium in the Vickrey-Clarke-Groves combinatorial auction mechanisms is a bundling equilibrium and is symmetric. This complements a theorem proved in Holzman, Kfir-Dahav, Monderer, and Tennenholtz [6], according to which, the symmetric bundling equilibria are precisely those defined by a quasi field.

* In the three linked articles Drs Clarke, Chambers, and Milne deal with the issue of using readmission rates as an outcome indicatorfor hospital care. Thefirst paper assesses thefeasibility ofmeasuring readmission ratesfrom routinely collected Korner data in a study of three districts in North East Thames region and the second, based on a study in one district, whether readmissions may be judg...