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.     

Structural Stability of Planar Polynomial Foliations

We discuss natural notions of structural stability of planar polynomial foliations of fixed degree with respect to perturbation within the same restricted set, within the set of all polynomial vector fields of the same degree, and within the set of smooth vector fields. Characterization theorems for structural stability in the latter two settings are obtained as immediate corollaries of known results. We provide sufficient conditions and separate necessary conditions for structural stability of planar polynomial foliations with respect to perturbation within the set of planar polynomial foliations of the same degree.     

Two-element laser beam expander

A simple laser beam expander is described which possesses several attractive features: there are only two optical elements; it is unobscured; it covers a wide spectral range with excellent performance; it can be made for any particular expansion ratio; and one of the two elements can usually be bought as an ‘off-the-shelf’ item.     

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.     

Immunomagnetic separation of tumor necrosis factor alpha. I. Batch procedure for human temporomandibular fluid.

A batch separation procedure has been developed for retrieval of tumor necrosis factor (TNF) alpha from the microliter volumes of fluid isolated from the human temporomandibular joint (TMJ). Paramagnetic beads coated with monoclonal antibodies for TNF were used. The beads, and bound TNF, were recovered from solution with the aid of a magnetic field. The amount of bead-bound TNF was quantified using an immuno-based assay developed in this laboratory called the cluster assay. The cluster assay was specific for TNF and linear up to 10 ng. Using these methods we found that TMJ fluid contained 0.2-4.2 ng per 100 microliters of fluid with a mean value of 1.9 ng and a standard deviation of 1.1 ng. This study demonstrates the utility of batch immunomagnetic separation for the concentration and purification of proteins, and the cluster assay for quantification of proteins from microliter volumes of body fluids.     

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.     

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.