Free Groups from Fields

In the nineteenth century, field theory brilliantly resolveda number of questions that had taxed mathematicians for centuries;for example, ‘The circle cannot be squared’ by straightedge and compass, and solving polynomial equations by radicalsis not always possible. These successes have continued to beheld up as superb examples of the power of mathematical thought,and are demonstrated at an undergraduate level. The purposeof this article is to provide another such natural example whichleads to a concrete realisation of the free group on 2 generators.     

Magnetic properties of amorphous alloys

The magnetic properties of existing amorphous iron based materials, i.e., Fe--metalloid, Fe--early transition metals and Fe--rare earth alloys, are briefly discussed for some representative alloys. The spin orientation of amorphous Fe--metalloid alloys has been determined by the angular dependence of hyperfine interactions. It is shown that in iron--early transition metals ferromagnetic order is not long-ranged, but determined by magnetic clusters. The magnetic hyperfine field distributions of Fe-rich iron--early transition metals consist of a high and a low field tail. The magnetic structure has been investigated for two representative Fe--RE (RE = Er, Ce) amorphous alloys. For the first time, the magnetic coupling phenomenon in amorphous/crystalline multilayers has been discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Molecular dynamics simulations of the oligonucleotide with the modified phosphate/phosphonate internucleotide linkage

Impact of the internucleotide linkage modification by inserting a methylene group to the P-O bond (—O—PO ₂ ^— —O— chain changed for —O—PO ₂ ^— —CH₂—O—), on the modified oligonucleotide binding ability to the natural DNA strand was studied by molecular dynamics simulation. Complex of (dT)₁₁ with a deoxyadenosine undecamer containing alternating modified and natural internucleotide linkage was studied as a model system. The Amber force field was completed by a set of new parameters needed to model the modified part of the nucleotide. The simulations confirmed existence of a double-helical complex the melting point of which is considerably higher than 300 K. While the thymidine (unmodified) strand possesses a B-type secondary structure, the conformation of the adenosine (modified) strand is not stable at 300 K. The -ggt conformation of the modified linkages is highly preferred, temporary jumps to the -g-gt and ggt conformations were, however, observed.     

Quadratic Functionals with General Boundary Conditions

The purpose of this paper is to give the Reid ``Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in [16] in terms of Riccati equation solutions. Accepted 27 February 1996     

Inclusive two-jet production at HERA: direct and resolved cross sections in next-to-leading order QCD

We have calculated inclusive two-jet cross sections in next-to-leading order QCD for low Q ² ep collisions superimposing direct and resolved contributions. Infrared and collinear singularities in the virtual and real contributions are cancelled with the phase space slicing method. Various inclusive two-jet distributions have been computed. The results are compared with recent data from the ZEUS collaboration at HERA.