A sequential sorting network analogous to the batcher merge

We present a network of delay log₂N, whose comparators have only log₂N different lengths with maximum length N/2. This network is log-sequential in that it will sort N data items when they are passed through it log₂Ntimes. The design, which is related to the Batcher odd-even merge, is distinctly different from the first known example of a log-delay log-sequential network, due to Dowd, Perl, Rudolf, and Saks. It is quite probably the best possible sorting network.     

Statistical inference and quantum mechanical measurement

We analyze the quantum mechanical measuring process from the standpoint of information theory. Statistical inference is used in order to define the most likely state of the measured system that is compatible with the readings of the measuring instrument and the a priori information about the correlations between the system and the instrument. This approach has the advantage that no reference to the time evolution of the combined system need be made. It must, however, be emphasized that the result is to be interpreted as the statistically inferred state of the original system rather than the state of the system after measurement. The phenomenon of “reduction of states” appears in this light as a consequence of incomplete information rather than the physical interaction between measured system and measuring instrument.     

Spontaneous staggered polarization of theF-model

The order parameter of the two-dimensionalF-model, namely the spontaneous staggered polarizationP ₀, is derived exactly. At the critical temperatureP ₀ has an essential singularity, bothP ₀ and all its derivatives with respect to temperature vanishing.     

THE ACTION SPECTRA OF FREE RADICALS PRODUCED BY THE IRRADIATION OF KERATIN CONTAINING BOUND IRON(III) IONS

Abstract—The action spectra have been determined for two free radical species produced by irradiating wool protein containing bound iron(III) ions with light between 330 and 540 nm. The faster growing free radical displays an action spectrum with a peak at 405–415 nm. It is suggested that an iron (III) ion-sulphur complex is the chromophore responsible for the formation of this carbon type radical.     

Proton capture by 15N at stellar energies

Excitation functions of the ¹⁵N(p, γ)¹⁶O proton capture reaction have been obtained at θ_γ = 45° and E_p = 150–2500 keV. Below E_p = 400 keV, the reaction is dominated by capture into the ground state of ¹⁶O. The observed excitation function for the latter process can be explained if, in addition to the two well-known J^π = 1^? resonances at E_p = 338 and 1028 keV, a direct radiative capture process (DC → 0) is included in the analysis. The direct capture component in the capture reaction is enhanced through interference effects on the tails of the two resonances. From the observed direct capture cross section, a single-particle spectroscopic factor of C²S(1p) = 1.8 ± 0.4 has been deduced for the ground state in ¹⁶O. The extrapolated astrophysical S-factor of S(0) = 64 ± 6 keV · b for the ¹⁵N(p, γ₀)¹⁶O reaction is a factor of 2.5 larger than previously reported. This result amplifies the role of the oxygen side cycle in the CNO hydrogen burning process.The observed excitation function of the ¹⁵N(p, α₁γ₁)¹²C reaction at E_p = 150 – 2500 keV shows that this reaction makes a negligible contribution to hydrogen burning at stellar energies [S(0) ≈ 0.1 keV · b] compared to ${}^{15}\text{N}\text{(}\text{p}\text{, γ}{}_0\text{)}{}^{16}\text{O and}{}^{15}\text{N}\text{(}\text{p}\text{, α}{}_{\mathrm{<mtext>o</mtext>}}\text{)}{}^{12}\text{C}$.     

Measurement of the streaming potential and streaming current near a rotating disk to determine its zeta potential

Methodology for determining the zeta potential of a disk-shaped sample by both streaming potential and streaming current measurements is presented. Integration of Laplace's equation within one radius of the disk surface revealed that the streaming potential decreased strongly in the surface normal direction. With this solution, the zeta potential can be calculated from measurements of the streaming potential near the surface of the disk provided the position of the working electrode near the disk surface is known. Determining the zeta potential of a disk-shaped sample by means of streaming current measurements required determination of a current collection efficiency because not all the streaming current from a disk flows through the auxiliary electronic current path. While the working electrode near the disk should be pointlike, several possible variants on counter electrode shape and size were explored. Although the current collection efficiency was only a few percent in each case, the measured current was of 10 nA order. The current collection efficiency depended only on system geometry and was independent of a disk's zeta potential and solution concentration. Streaming current measurements of zeta potential on silicon wafers in potassium chloride solutions up to 10 mM agreed well with published values.     

Long range 13C shift effects (δ and ϵ) in methylcyclohexanes

¹³C n.m.r. spectra of a number of methyl substituted cyclohexanes, some of them conformationally homogeneous, have been recorded in CDCl₃ and used to determine shift effects engendered by the introduction of methyl groups on carbon atoms remote from the site of substitution. Sizeable changes in shifts are found, including a substantial effect of an equatorial methyl group on an axial methyl group δ to it (+0.6₇ ppm, ‘δ_ea’). The effects reported are of consequence in investigations of conformational problems by ¹³C n.m.r. techniques.