Tropical convexity via cellular resolutions

The tropical convex hull of a finite set of points in tropical projective space has a natural structure of a cellular free resolution. Therefore, methods from computational commutative algebra can be used to compute tropical convex hulls. Tropical cyclic polytopes are also presented.     

A new model for auroral breakup during substorms

A model for substorm breakup is developed, based on (1) the relaxation of stretched (closed) dipolar field lines, and (2) the formation of an incipient current wedge within a single arc structure. It is argued that the establishment of a coupled current structure within a single arc leads to a quasistable system, i.e. the prebreakup regime. Perturbation of the prebreakup structure leads to an instability criterion. It is found, consistent with observations, that the narrower auroral arcs at lower L shells undergo the most explosive poleward expansion. According to this model, the precise location at which breakup occurs depends on the O⁺ density in the plasma sheet, the level of magnetic activity (K_p), and the intensity of the substorm westward electrojet in the ionosphere. An enhancement of any of these features will cause breakup to occur at lower L shells. Comparison of the proposed model with the Heppner-Maynard polar-cap potential model indicates that breakup is restricted to the west of the Harang discontinuity, consistent with observations from the Viking satellite     

Computing the topological entropy of maps of the interval with three monotone pieces

An algorithm is presented for computing the topological entropy of a piecewise monotone map of the interval having three monotone pieces. The accuracy of the algorithm is discussed and some graphs of the topological entropy obtained using the algorithm are displayed. Some of the ideas behind the algorithm have application to piecewise monotone functions with more than three monotone pieces.     

Electron spin resonance study of free radicals in the radiation grafting of butadiene to poly(vinyl chloride)

The kinetics of the disappearance of propagating butadiene radicals produced in the grafting of butadiene to poly(vinyl chloride) was followed by electron spin resonance measurements. The radical species observed in the temperature range 213–298°K is the conjugated allylic radical: The reaction conditions were adjusted to provide a highly viscous medium in which the propagation reaction took place. Under these conditions the radicals were stabilized and a precise ESR spectrum was obtained. Arrhenius plots of the second-order decay rate constants yield an activation energy of 5 kcal/mole. This suggests that the bimolecular termination reaction is controlled by the segmental motion of the grafted side chains.     

Extended Born-Green equation: A new approach for determining pair potentials in disordered systems

The Born-Green equation was tested using molecular dynamics data for liquid rubidium at 319 K. The unsatisfactory results of this equation for the pair potential are caused by the insufficient precision of the Kirkwood approximation for describing the triplet correlation function g₃(r,s,t). A more realistic ansatz for g₃(r,s,t) was employed in the formulation of an extended Born-Green equation. This new approach gives much better results for the potential than the simple Born-Green equation.     

Upper limit for DD production in pp interactions at C.M. energy of 55 GeV

From a search for e^±μ^± production at the CERN ISR an upper limit of 0.92 μb (95% confidence limit) has been inferred for σ·B_e·B_μ for the reaction $\text{p}\text{+}\text{p}\text{→}\text{D}\text{+}\text{D}\text{+}\text{X}\text{at}\text{√s}\text{of}\text{55}\text{GeV}$.     

Feldionen-Mikroskopie und Massen-Spektroskopie von schwefelbedeckten Ag-Oberfl?chen

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