The Poincare mass operator in terms of a hyperbolic algebra

The Poincare mass operator can be represented in terms of a Cl(3,0) Clifford algebra. With this representation the quadratic Dirac equation and the Maxwell equations can be derived from the same mathematical structure.Comment: 5 pages Latex2

A second order differential equation for the relativistic description of electrons and photons

A new relativistic description of quantum electrodynamics is presented. Guideline of the theory is the Klein-Gordon equation, which is reformulated to consider spin effects. This is achieved by a representation of relativistic vectors with a space-time algebra made up of Pauli matrices and hyperbolic numbers. The algebra is used to construct the differential operator of the electron as well as the photon wave equation. The properties of free electron and photon states related to this wave equation are investigated. Interactions are introduced as usual with the minimal substitution of the momentum operators. It can be shown that the new wave equation is equivalent to the quadratic form of the Dirac equation. Furthermore, the Maxwell equations can be derived from the corresponding wave equation for photons.Comment: Reverted preprint to initial version of 1999. Most of the content has been published under the new title "Relativistic quantum physics with hyperbolic numbers". However, interesting parts like the second quantization of fermion fields within a Klein-Gordon theory, which is only possible with the help of hyperbolic or bicomplex numbers, dropped out of the revised versio

Network Congestion Effect of E-Hailing Transportation Services

E-hailing plays a key role in emerging transportation services such as ridesourcing, ridesharing and taxis, among others. This seminar will present a general economic model to analyze the congestion effect of e-hailing services in a transportation network. The model can help analyze customers’ choices of different modes, based on their value of time and the charging schemes of different services, as well as the overall impact of the services to network level congestion.https://pdxscholar.library.pdx.edu/trec_seminar/1119/thumbnail.jp

Comparison of Conventional Double-Helical and Curvilinear Cylindrical Gear Drives in Terms of Transmission Errors and Stress

Curvilinear cylindrical gear drives are similar to double-helical gear drives as they can avoid the axial thrust during the meshing process. Whether curvilinear cylindrical gear drives are better than double-helical gear drives is a problem to be solved. In this paper, a new gear-generating method for curvilinear gears is proposed based on the theory of gearing. Two different single-side face-milling cutters are used for the generation of concave and convex tooth surfaces, respectively. The curvilinear gear sets being generated have line contact in the meshing process. For the sake of comparison, the double-helical gear sets involved in the comparison study are also a kind of gear sets with line contact. This article includes the following: (1) Comparison of transmission errors and stresses of two types of gear sets with the same contact ratio; (2) Derivation of tooth surface equations, transmission error analysis, and finite element analysis; (3) Four numerical examples which show the advantages and disadvantages of curvilinear cylindrical gear drives