Mass spectrometer with magnetic pole pieces providing the magnetic fields for both the magnetic sector and an ion-type vacuum pump

A mass spectrometer (MS) with unique magnetic pole pieces which provide a homogenous magnetic field across the gap of the MS magnetic sector as well as the magnetic field across an ion-type vacuum pump is disclosed. The pole pieces form the top and bottom sides of a housing. The housing is positioned so that portions of the pole pieces form part of the magnetic sector with the space between them defining the gap region of the magnetic sector, through which an ion beam passes. The pole pieces extend beyond the magnetic sector with the space between them being large enough to accommodate the electrical parts of an ion-type vacuum pump. The pole pieces which provide the magnetic field for the pump, together with the housing form the vacuum pump enclosure or housing

Efficient Finite Groups Arising in the Study of Relative Asphericity

We study a class of two-generator two-relator groups, denoted Jn(m, k), that arise in the study of relative asphericity as groups satisfying a transitional curvature condition. Particular instances of these groups occur in the literature as finite groups of intriguing orders. Here we find infinite families of non-elementary virtually free groups and of finite metabelian non-nilpotent groups, for which we determine the orders. All Mersenne primes arise as factors of the orders of the non-metacyclic groups in the class, as do all primes from other conjecturally infinite families of primes. We classify the finite groups up to isomorphism and show that our class overlaps and extends a class of groups Fa,b,c with trivalent Cayley graphs that was introduced by C.M.Campbell, H.S.M.Coxeter, and E.F.Robertson. The theory of cyclically presented groups informs our methods and we extend part of this theory (namely, on connections with polynomial resultants) to ?bicyclically presented groups? that arise naturally in our analysis. As a corollary to our main results we obtain new infinite families of finite metacyclic generalized Fibonacci groups

Nash implementation through elementary mechanisms in economic environments

Nash implementation, Social choice correspondence, Elementary mechanism, Economic environment, C72, D51, D78, H40,