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You searched for +publisher:"University of Oklahoma" +contributor:("Cruz, J.R."). Showing records 1 – 2 of 2 total matches.

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University of Oklahoma

1. Shukla, Alok. On Klingen Eisenstein series with levels.

Degree: PhD, 2018, University of Oklahoma

We give a representation theoretic approach to the Klingen lift generalizing the classical construction of Klingen Eisenstein series to arbitrary level for both paramodular and Siegel congruence subgroups. Moreover, we give a computational algorithm for describing the one-dimensional cusps of the Satake compactifications for the Siegel congruence subgroups in the case of degree two for arbitrary levels. As an application of the results thus obtained, we calculate the co-dimensions of the spaces of cusp forms in the spaces of modular forms of degree two with respect to Siegel congruence subgroups of levels not divisible by 8. Advisors/Committee Members: Schmidt, Ralf (advisor), Cruz, J.R. (committee member), Pitale, Ameya (committee member), Przebinda, Tomasz (committee member), Roche, Alan (committee member).

Subjects/Keywords: Mathematics; Automorphic Representation; Klingen Eisenstein Series with levels; Paramodular; Co-dimension formula for cusp forms

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APA (6th Edition):

Shukla, A. (2018). On Klingen Eisenstein series with levels. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/299326

Chicago Manual of Style (16th Edition):

Shukla, Alok. “On Klingen Eisenstein series with levels.” 2018. Doctoral Dissertation, University of Oklahoma. Accessed April 18, 2021. http://hdl.handle.net/11244/299326.

MLA Handbook (7th Edition):

Shukla, Alok. “On Klingen Eisenstein series with levels.” 2018. Web. 18 Apr 2021.

Vancouver:

Shukla A. On Klingen Eisenstein series with levels. [Internet] [Doctoral dissertation]. University of Oklahoma; 2018. [cited 2021 Apr 18]. Available from: http://hdl.handle.net/11244/299326.

Council of Science Editors:

Shukla A. On Klingen Eisenstein series with levels. [Doctoral Dissertation]. University of Oklahoma; 2018. Available from: http://hdl.handle.net/11244/299326


University of Oklahoma

2. Zhu, Ye. Radar cross section modeling of tornadic debris and applications.

Degree: PhD, 2016, University of Oklahoma

Tornadic debris plays an important role in the study of tornadoes due to the dramatic threat it poses to human life, and the devastation it causes to commercial and residential property. Radar cross section (RCS) modeling on plate-like and cylindrical objects is developed in this tornadic debris study. The sheets, plates, and cylinders used in this study are designed to represent leaves, wood board, flat building forms, metal rods, tree trunks, and branches, respectively. Different techniques are evaluated in terms of the geometry of the object, accuracy, and math complexity and computation efficiency. Geometrical Optics (GO), Geometrical Theory of Diffraction (GTD), Finite Element Method (FEM), Finite Difference Time Domain method (FDTD), Moment of Method (MoM) and Physical Optics (PO) are introduced. Finally, the decision to use PO for deriving the formulation for plate-like objects throughout the dissertation was made. Non-metal objects such as cylinder broadside, endcap, general circular sheets and plates, surface impedance circular plates, rectangular sheets and plates, as well as metal circular plates are derived by hand. Metal objects such as cylinder broadside and rectangular plates, as well as resistive rectangular thin sheet approximations, are verified and cited from published research books and papers. Full wave simulation Ansys HFSS validates the analytical results in most cases. FEKO commercial software is used to compare the analytical results for two layer plates with different media and leaf sample applications. After testing, metal vs. non-metal plates and thin vs. thick plates are distinguished by 5 dB, 10 dB, and 20 dB from the simulation results, respectively; this fact confirms the accuracy and limitations of theory. By adding endcaps, one is able to compensate the deficiency from normal to the cap surface of the finite cylinder by at least several wavelengths in length and at least half of a wavelength in radius. The theoretical analysis of the extension of PO indicates that more accurate results appear as the incident angle gets closer to normal. The errors and limitations of PO are described and demonstrated by comparison plots of analytical results vs. HFSS throughout. The leaf library and wood board (dry and wet) studies are performed as sample applications for “real” debris types under the radar coordinate transformation system for all polarizations at oblique TEM incident wave. Research questions are answered in the conclusions. Advisors/Committee Members: Cruz, J.R (advisor), Palmer, Robert (committee member), Yang, Zhibo (committee member), Fulton, Caleb (committee member), Yeary, Mark (committee member).

Subjects/Keywords: radar cross section modeling, debris scatterer, plate-like and cylindrical objects, HFSS, FEKO, modeling applications; Physical Optics technique

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Zhu, Y. (2016). Radar cross section modeling of tornadic debris and applications. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/34599

Chicago Manual of Style (16th Edition):

Zhu, Ye. “Radar cross section modeling of tornadic debris and applications.” 2016. Doctoral Dissertation, University of Oklahoma. Accessed April 18, 2021. http://hdl.handle.net/11244/34599.

MLA Handbook (7th Edition):

Zhu, Ye. “Radar cross section modeling of tornadic debris and applications.” 2016. Web. 18 Apr 2021.

Vancouver:

Zhu Y. Radar cross section modeling of tornadic debris and applications. [Internet] [Doctoral dissertation]. University of Oklahoma; 2016. [cited 2021 Apr 18]. Available from: http://hdl.handle.net/11244/34599.

Council of Science Editors:

Zhu Y. Radar cross section modeling of tornadic debris and applications. [Doctoral Dissertation]. University of Oklahoma; 2016. Available from: http://hdl.handle.net/11244/34599

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