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Full-Text Articles in Physical Sciences and Mathematics
What Does Height Really Mean? Part Iv: Gps Orthometric Heighting, Thomas H. Meyer, Daniel R. Roman, David B. Zilkoski
What Does Height Really Mean? Part Iv: Gps Orthometric Heighting, Thomas H. Meyer, Daniel R. Roman, David B. Zilkoski
Department of Natural Resources and the Environment Articles
This is the final paper in a four-part series examining the fundamental question, “What does the word height really mean?” The creation of this series was motivated by the National Geodetic Survey’s (NGS) embarking on a height modernization program as a result of which NGS will publish measured ellipsoid heights and computed Helmert orthometric heights for vertical bench marks. Practicing surveyors will therefore encounter Helmert orthometric heights computed from Global Positioning System (GPS) ellipsoid heights and geoid heights determined from geoid models as their published vertical control coordinate, rather than adjusted orthometric heights determined by spirit leveling. It is our …
Fourier Series, Examples And The Fourier Integral, Carl W. David
Fourier Series, Examples And The Fourier Integral, Carl W. David
Chemistry Education Materials
The derivation of the Fourier Integral from the Fourier series in complex form is carried out and illustrations of the Fourier Integral are done.
The Tensor Of The Moment Of Inertia, Carl W. David
The Tensor Of The Moment Of Inertia, Carl W. David
Chemistry Education Materials
The tensor of the moment of inertia for polyatomic molecules is presented, discussed, and illustrated.
The Harmonic Oscillator, The Hermite Polynomial Solutions, Carl W. David
The Harmonic Oscillator, The Hermite Polynomial Solutions, Carl W. David
Chemistry Education Materials
The Hermite polynomial solution to the simple harmonic oscillator is discussed.
The Harmonic Oscillator, The Ladder Operator Solutions, Carl W. David
The Harmonic Oscillator, The Ladder Operator Solutions, Carl W. David
Chemistry Education Materials
The ladder operator approach to the quantum mechanics of the simple harmonic oscillator is presented.
The Runge-Lenz Vector, Carl W. David
The Runge-Lenz Vector, Carl W. David
Chemistry Education Materials
The Runge-Lenz vector is a constant of the motion in the Kepler problem. As a precursor to developing a ladder operator formalism for the H-atom's quantum mechanics, various relations concerning the Runge-Lenz vector are obtained.
The Particle In A Box (And In A Circular Box), Carl W. David
The Particle In A Box (And In A Circular Box), Carl W. David
Chemistry Education Materials
The particle in a box problem in 1 and 2 dimensions is treated both for the Cartesian problem (square, rectangle) but for circular boundary conditions.
The Hamiltonian And Schrodinger Equation For Helium's Electrons (Hylleraas), Carl W. David
The Hamiltonian And Schrodinger Equation For Helium's Electrons (Hylleraas), Carl W. David
Chemistry Education Materials
The Hylleraas forms for the kinetic energy operator for the two electrons of Helium in the ground singlet Sigma state are obtained explicitly.
The Hasse-Minkowski Theorem, Adam Gamzon
The Hasse-Minkowski Theorem, Adam Gamzon
Honors Scholar Theses
The Hasse-Minkowski theorem concerns the classification of quadratic forms over global fields (i.e., finite extensions of Q and rational function fields with a finite constant field). Hasse proved the theorem over the rational numbers in his Ph.D. thesis in 1921. He extended the research of his thesis to quadratic forms over all number fields in 1924. Historically, the Hasse-Minkowski theorem was the first notable application of p-adic fields that caught the attention of a wide mathematical audience. The goal of this thesis is to discuss the Hasse-Minkowski theorem over the rational numbers and over the rational function fields with a …