Evidence for polarised boron in Co-B and Fe-B alloys

By exploiting the tunability of synchrotron radiation in measurements of spin-resolved photoemission it has proved possible to obtain information on the polarisation of the valence electrons of Co-B and Fe-B amorphous magnetic alloys, Both the spin-integrated and spin-resolved energy distribution curves show a marked dependence on photon energy indicating that the p states of boron hybridise with the d states of the transition metals giving rise to mixed states in the binding energy range 1 to 5 eV, The observed polarisation and spin-resolved densities of states imply that in the above restricted energy range there is a net negative polarisation of the boron states

Yang-Mills action from minimally coupled bosons on R^4 and on the 4D Moyal plane

We consider bosons on Euclidean R^4 that are minimally coupled to an external Yang-Mills field. We compute the logarithmically divergent part of the cut-off regularized quantum effective action of this system. We confirm the known result that this term is proportional to the Yang-Mills action. We use pseudodifferential operator methods throughout to prepare the ground for a generalization of our calculation to the noncommutative four-dimensional Moyal plane (also known as noncommutative flat space). We also include a detailed comparison of our cut-off regularization to heat kernel techniques. In the case of the noncommutative space, we complement the usual technique of asymptotic expansion in the momentum variable with operator theoretic arguments in order to keep separated quantum from noncommutativity effects. We show that the result from the commutative space R^4 still holds if one replaces all pointwise products by the noncommutative Moyal product.Comment: 37 pages, v2 contains an improved treatment of the theta function in Appendix A.

Divide and Conquer

The maxim “divide and conquer” (divide et impera) is invoked frequently in law, history, and politics, but often in a loose or undertheorized way. We suggest that the maxim is a placeholder for a complex of ideas related by a family resemblance, but differing in their details, mechanisms and implications. We provide an analytic taxonomy of divide and conquer mechanisms in the settings of a Stag Hunt Game and an indefinitely-repeated Prisoners' Dilemma. A number of applications are considered, including labor law, bankruptcy, constitutional design and the separation of powers, imperialism and race relations, international law, litigation and settlement, and antitrust law. Conditions under which divide and conquer strategies reduce or enhance social welfare, and techniques that policy makers can use to combat divide and conquer tactics, are also discussed