On skew field coproducts with a finite extension

It is shown that the field coproduct of any skew fieldE with a binomial (commutative) field extensionF/k overk can be expressed as a cyclic extension of a skew fieldK (theE-socle), itself the field coproduct of [F:k] copies ofE overk. Qua vector space the coproduct may also be expressed as a tensor product ofE andK overk. To the memory of Shimshon Amitsur     

Classical tunneling

A classical representation of an extended body over barriers of height greater than the energy of the incident body is shown to have many features in common with quantum tunneling as the center-of-mass literally goes through the barrier. It is even classically possible to penetrate any finite barrier with a body of arbitrarily low energy if the body is sufficiently long. A distribution of body lengths around the de Broglie wavelength leads to reasonable agreement with the quantum transmission coefficient.     

Possible high-frequency cavity and waveguide applications of high temperature superconductors

Conventional superconducting materials used at liquid helium temperatures have been employed to greatly reduce ohmic power loss in microwave cavities. If suitable high temperature superconductor surfaces can be developed, it could be possible to alleviate constraints due to relatively low energy gaps and limits due to critical fields, and operate at more convenient temperatures with larger thermal margins. These features could be used to improve performance of present superconducting microwave cavity devices. They may also facilitate new applications and device designs at millimeter-wave and far infrared frequencies. Possible cavity and waveguide applications are described. Sensitivity of RF surface resistance to boundaries and nonaligned grains in the material and to small amounts of nonsuperconducting material may be an obstacle to development. Moreover, critical RF fields can be limiting for high power applications. An additional problem is the adverse effect of D.C. magnetic fields.Supported by Department of Energy No. ET-51013-227. Reproduction, translation, publication, use and disposal in whole or in part, by or for the United States government is permitted.     

Holistic electron theory

A relativistic, non-quantum theory of electrons is constructed in which the electron is not considered to be composed of any type of distribution of charge. The electron's structurelessness is defined by several assumptions which, together with Maxwell's equations outside the electron, yield the general fields produced by such an arbitrarily movingholistic electron. Several equations of motion for the holistic electron are found to result from the formulation, the Lorentz-Dirac equation being among them. The formulation, by its very nature, avoids the problems of the electron self-energy and the need for normalization.     

Ternary forms as invariants of Markoff forms and other SL2 (Z)-bundles

Consider the free group Γ = {A,B} generated by matrices A, B in SL₂(Z). We can construct a ternary form Φ(x,y,z) whose GL₃(Z) equivalence class is invariant, as it depends on Γ and not the choice of generators. If Γ is the commutator of SL₂(Z), then the generating matrices have fixed points corresponding to different fields and inequivalent Markoff forms, but they are all biuniquely determined by Φ = -z²+ y(2x+y+z) to within equivalence. When referred to transformations A, B of the upper half plane, this phenomenon is interpreted in terms of inequivalent homotopy elements which are primitive for the perforated torus.     

Determination of demecarium bromide and related compounds by high-performance liquid chromatography

A high-performance liquid chromatographic method for the determination of demecarium bromide and related process intermediate and companion products is described. The compounds of interest are separated by isocratic reversed-phase chromatography on a mu Bondapak CN column using UV detection. The reproducibility of the method and stability of demecarium bromide is demonstrated. Applications presented for the method include quantitation of demecarium bromide in aqueous solutions and control of the raw material.     

Respiratory and glottal efficiency measures in normal classically trained singers

Respiratory and glottal efficiency measures were collected from a pool of 40 classically trained singers with normal larynges. All singers had ?3 years of formal classical voice training and were active professional solo classical singers. Mean flow rates were obtained from all subjects to assess glottal efficiency. Additionally, maximum phonation times and phonation quotients were obtained from a subset of the singers. Pulmonary function test data on forced expiratory volume, forced vital capacity, and forced expiratory flow were obtained for all subjects. Results were compared with published normal values, not specifically derived from trained singers, used commonly in voice laboratoires. Differences were found, suggesting the need for separate normative data to be used for evaluation of the vocal athlete.