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Virginia Tech

1. Miller, Nicole Renee. The Structure of the Class Group of Imaginary Quadratic Fields.

Degree: MS, Mathematics, 2005, Virginia Tech

Let Q(√{-d}) be an imaginary quadratic field with discriminant Δ. We use the isomorphism between the ideal class groups of the field and the equivalence classes of binary quadratic forms to find the structure of the class group. We determine the structure by combining two of Shanks' algorithms [7, 8]. We utilize this method to find fields with cyclic factors that have order a large power of 2, or fields with class groups of high 5-ranks or high 7-ranks. Advisors/Committee Members: Parry, Charles J. (committeechair), Haskell, Peter E. (committee member), Brown, Ezra A. (committee member).

Subjects/Keywords: 7-rank; 5-rank; Positive Definite Forms; Genera; Class Group; Binary Quadratic Fields

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

APA (6th Edition):

Miller, N. R. (2005). The Structure of the Class Group of Imaginary Quadratic Fields. (Masters Thesis). Virginia Tech. Retrieved from http://hdl.handle.net/10919/32572

Chicago Manual of Style (16th Edition):

Miller, Nicole Renee. “The Structure of the Class Group of Imaginary Quadratic Fields.” 2005. Masters Thesis, Virginia Tech. Accessed July 15, 2020. http://hdl.handle.net/10919/32572.

MLA Handbook (7th Edition):

Miller, Nicole Renee. “The Structure of the Class Group of Imaginary Quadratic Fields.” 2005. Web. 15 Jul 2020.

Vancouver:

Miller NR. The Structure of the Class Group of Imaginary Quadratic Fields. [Internet] [Masters thesis]. Virginia Tech; 2005. [cited 2020 Jul 15]. Available from: http://hdl.handle.net/10919/32572.

Council of Science Editors:

Miller NR. The Structure of the Class Group of Imaginary Quadratic Fields. [Masters Thesis]. Virginia Tech; 2005. Available from: http://hdl.handle.net/10919/32572

2. Fuji, Hiroaki. Necrostatin-7 suppresses RANK-NFATc1 signaling and attenuates macrophage to osteoclast differentiation .

Degree: 2019, Kyoto University

Subjects/Keywords: Macrophage; Osteoclast; RANK; RANKL; NFATc1; Necrostatin-7

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

APA (6th Edition):

Fuji, H. (2019). Necrostatin-7 suppresses RANK-NFATc1 signaling and attenuates macrophage to osteoclast differentiation . (Thesis). Kyoto University. Retrieved from http://hdl.handle.net/2433/242355

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Fuji, Hiroaki. “Necrostatin-7 suppresses RANK-NFATc1 signaling and attenuates macrophage to osteoclast differentiation .” 2019. Thesis, Kyoto University. Accessed July 15, 2020. http://hdl.handle.net/2433/242355.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Fuji, Hiroaki. “Necrostatin-7 suppresses RANK-NFATc1 signaling and attenuates macrophage to osteoclast differentiation .” 2019. Web. 15 Jul 2020.

Vancouver:

Fuji H. Necrostatin-7 suppresses RANK-NFATc1 signaling and attenuates macrophage to osteoclast differentiation . [Internet] [Thesis]. Kyoto University; 2019. [cited 2020 Jul 15]. Available from: http://hdl.handle.net/2433/242355.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Fuji H. Necrostatin-7 suppresses RANK-NFATc1 signaling and attenuates macrophage to osteoclast differentiation . [Thesis]. Kyoto University; 2019. Available from: http://hdl.handle.net/2433/242355

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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