The steiner minimal network for convex configurations

SupposeX is a convex configuration with radius of maximum curvaturer and at most one of the edges joining neighboring points has length strictly greater thanr. We use the variational approach to show the Steiner treeS coincides with the minimal spanning tree and consists of all these edges with a longest edge removed. This generalizes Graham's problem for points on a circle, which we had solved. In addition we describe the minimal spanning tree for certain convex configurations.     

Cross section measurements of the Pd(p, γ)Ag, Sn(p, γ)Sb, and Sn(α, γ)Te reactions relevant to the astrophysical rp- and γ-processes

Total cross section measurements for the ¹⁰²Pd(p, γ)¹⁰³Ag and ¹¹⁶Sn(p, γ)¹¹⁷Sb reactions have been performed in the proton energy range 2.6 to 4.25 MeV, and for the ¹¹²Sn(α, γ)¹¹⁶Te reaction over the alpha beam energy range 7.0 to 10.5 MeV. An activation technique was used in which gamma rays from decays of the reaction products were detected off-line by two hyper-pure germanium detectors in a low background environment. Where possible, reaction rates are derived and the results compared to those of calculations generated by the NON-SMOKER and the MOST statistical model codes so as to judge their applicability for describing the cross sections needed for network calculations of nucleosynthesis in explosive astrophysical environments via the γ- and rp-processes.     

Adsorption of polymers at the solution-solid interface. VII. Poly(acrylic acids), model compounds,and vapors on nylon fibers

Nylon fibers of various draw ratios have been used as the adsorbents in the adsorption of low molecular weight acids and of polyacrylic acids from solution. Polymer adsorption is lower than on a precipitated nylon and decreases with fiber orientation; however, propionic acid and glutaric acids do not show this dependence on nylon structure. The structural alterations consequent on fiber drawing also reduce swelling in hydroxylated liquids. The greater accessibility of the precipitated nylon is shown by vapor sorption and extends to nonhydroxylated vapors; however, the differences in behavior between polyamide powder and fiber cannot be fully attributed to the former possessing a porous structure, in the sense normally employed in surface chemistry.     

NMR studies of silver ion and 1,3,5-trinitrobenzene complexes

A study, using NMR techniques, of the propensity of complex formation of silver ions with hydrocarbons and heterocyclic compounds containing nitrogen, oxygen and sulphur is described. The results are compared with similar data using 1,3,5-trinitrobenzene as an acceptor. The differences in the two sets of data are interpreted in terms of localized and delocalized interactions in the formation of weak complexes.     

Semiempirical determination of the atom-surface interaction

We discuss three methods of determining V(z), the lateral average (G = 0 Fourier component) of the atom-surface interaction, from the bound state spectrum found in beam scattering. One method uses the Rydberg-Klein-Rees technique, which yields the width of the potential (i.e., separation of classical turning points) as a function of energy. This method incorporates also the known asymptotic form V ～ ?C₃z^?3, whereC₃ is derived from the polarizability and dielectric function of atom and solid, respectively. The second method uses a hybrid potential, constructed from a Morse potential with shifted zero of energy connected to the asymptotic form,?C₃z^?3, requiring continuity of V and $\text{d}\text{V}\text{d}\text{z}$. The third potential is a Lennard-Jones 3–9 interaction. Results are presented for H and He scattering from LiF and NaF.     

Six-dimensional Dirac equation

The Dirac equation in six-dimensional relativity (three space and three time) is considered and shown to correspond to particles which have spatial spin-1/2 and temporal spin-1/2. Explicit forms of the spinor transformation are found. Plane wave solutions are obtained and their properties are given in terms of spatial and temporal spins and helicities. An expression is found for the charge conjugation operator.     

Giant resonances in f-p shell nuclei studied by inelastic scattering of 80 MeV 3He ions

Spectra of ⁴⁸Ti, ⁵⁶Fe, ⁵⁹Co and ⁶⁰Ni have been investigated for excitation energies of 10–20 MeV by inelastic scattering of 80 MeV ³He particles. Broad peaks with excitation energies of about $\text{63±1 A}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}\text{MeV}$ and FWHM of 6 MeV have been observed. Much narrower satellite peaks occur at excitation energies about $\text{51±1 A}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}\text{MeV}$. The angular distributions of the sum of these peaks were compared to extended optical model DWBA calculations which confirm the predominant L = 2 character of the GR. A tentative assignment of L = 2 or 4 was made for the 13.5 MeV satellite peak in ⁵⁶Fe. We see no definite evidence for the presence of an L = 1 GR component.     

High resolution proton magnetic resonance spectra of heterocyclics 1,4-benzodithiin and 1,4-benzodioxin

The proton magnetic resonance spectra of 1,4-benzodithiin and 1,4-benzodioxin have been fully analyzed. The effects of the substituent heteroatoms on the chemical shifts of the various protons in the two molecules have been discussed.     

A method for predicting the stability characteristics of three-term homogeneous recurrence relations

A simple method is presented which determines the numerical stability or instability in the computation of any solution of a three-term homogeneous linear difference equation of order m in terms of the size of a single parameter. The method is illustrated by application to a second order and to a third order difference equation. Excellent agreement with predictions is reported.