Lévy’s Zero–One Law in Game-Theoretic Probability

We prove a nonstochastic version of Lévy’s zero–one law and deduce several corollaries from it, including nonstochastic versions of Kolmogorov’s zero–one law and the ergodicity of Bernoulli shifts. Our secondary goal is to explore the basic definitions of game-theoretic probability theory, with Lévy’s zero–one law serving a useful role.     

Raman results in the superionic conductor RbAg4I5

Raman measurements between 77°K and 296°K are reported for the superionic conductor RbAg₄I₅. Careful attention is paid to the temperature region of the two phase transitions at 121°K and 208°K. We can detect no shifts in any of the numerous phonon modes except one at 22.9 cm^-1, which abruptly and reversibly appears in the lowest temperature phase. Raman results for the isomorphic material KAg₄I₅ are the same with the same mode appearing in the low temperature phase. Thus, the results in these systems are markedly different from those in AgI, where there are very large changes at the superionic conducting transition temperature.     

Energy storage effect and retrieval in manganese doped zinc silicate

It is shown that a significant amount of energy can be stored at room temperature for long periods in the manganese activated zinc silicates upon excitation by short wavelength UV photons (>3.65eV), and X-ray radiation. The stored energy can be stimulated by long wavelength photons (infrared and red) resulting in visible green emission. This effect has potential application in high energy radiation detection and imaging.     

Examination of the various crystal field theories of d3 ions in trigonal fields

Zero-field splitting and g-anisotropy of the ground multiplet of HfS₂(V²⁺) have been measured by electron paramagnetic resonance. The unusually large g-anisotropy and its relationship to the zero-field splitting alow a comparison between various crystal field theories. We find that the experimental results are in disagreement with the simple crystal field theory of Van Vleck for the ground multiplet of d³ ions in trigonally distroted octahedral environments, but in reasonable agreement with the more elaborate but straightforward crystal field theory of Macfarlane. We thus conclude that it is unnecessary to resort to an anisotropic spin-orbit coupling as suggested by Sugano and Tanabe or to odd-parity crystal field terms as suggested by Artman and Murphy.     

Conformational analysis of tertiary cycloalkyl (C6,C7,C8) carbocations using molecular mechanics. Comparison with stable ion experimental data

Conformational calculations of the 1-methylcyclohexyl, 1-methylcycloheptyl, and 1-methylcyclooctyl cations agree with reported experimental observations.     

Analysis of the 1H NMR spectrum of α-tetralone

An analysis of both the aromatic and aliphatic portions of the ¹H NMR spectrum of α-tetralone has been carried out. Two deuterated derivatives, 2,2-dideuterio- and 4,4-dideuterio-α-tetralone, were prepared to facilitate unambiguous assignment of chemical shifts for the aliphatic protons. The conformation of the 6-membered alicyclic ring of the molecule is defined by the coupling constants among the aliphatic protons. Benzylic coupling was the only detectable long range interaction between the aliphatic and aromatic protons of the molecule. The magnitude and sign of these coupling constants agree with previous calculations of Wasylishen and Schaefer.     

Multiplexed Readout of Superconducting Bolometers

Studies of emission in the far-infrared and submillimeter from astrophysical sources require large arrays of detectors containing hundreds to thousands of elements. A multiplexed readout is necessary for practical implementation of such arrays, and can be developed using SQUIDS, such that, e.g., a 32 × 32 array of bolometers can be read out using 100 wires rather than the >2000 needed with a brute force expansion of existing arrays. These bolometer arrays are made by micromachining techniques, using superconducting transition edge sensors as the thermistors. We describe the development of this multiplexed superconducting bolometer array architecture as a step toward bringing about the first astronomically useful arrays of this design. This technology will be used in the SAFIRE instrument on SOFIA, and is a candidate for a wide variety of other spectroscopic and photometric instruments.     

Menger’s theorem in {{\Pi^1_1\tt{-CA}_0}}

We prove Menger’s theorem for countable graphs in ${{\Pi^1_1\tt{-CA}_0}}$ . Our proof in fact proves a stronger statement, which we call extended Menger’s theorem, that is equivalent to ${{\Pi^1_1\tt{-CA}_0}}$ over ${{\tt{RCA}_0}}$ .