subject:(Theta functions)

Hong Kong University of Science and Technology

1. Bao, Yixin. The explicit theta correspondence for reductive dual pairs (Sp(p,q),O*(4)).

Degree: 2014, Hong Kong University of Science and Technology

URL: https://doi.org/10.14711/thesis-b1334878 ; http://repository.ust.hk/ir/bitstream/1783.1-71826/1/th_redirect.html

► In this thesis I will describe the theta correspondence for the reductive dual pairs (Sp(p,q),O^*(4)) in terms of Langlands parameters. For the general reductive dual… (more)

Subjects/Keywords: Functions, Theta; Representations of groups

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

APA (6^th Edition):

Bao, Y. (2014). The explicit theta correspondence for reductive dual pairs (Sp(p,q),O*(4)). (Thesis). Hong Kong University of Science and Technology. Retrieved from https://doi.org/10.14711/thesis-b1334878 ; http://repository.ust.hk/ir/bitstream/1783.1-71826/1/th_redirect.html

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

Chicago Manual of Style (16^th Edition):

Bao, Yixin. “The explicit theta correspondence for reductive dual pairs (Sp(p,q),O*(4)).” 2014. Thesis, Hong Kong University of Science and Technology. Accessed December 12, 2019. https://doi.org/10.14711/thesis-b1334878 ; http://repository.ust.hk/ir/bitstream/1783.1-71826/1/th_redirect.html.

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

MLA Handbook (7^th Edition):

Bao, Yixin. “The explicit theta correspondence for reductive dual pairs (Sp(p,q),O*(4)).” 2014. Web. 12 Dec 2019.

Vancouver:

Bao Y. The explicit theta correspondence for reductive dual pairs (Sp(p,q),O*(4)). [Internet] [Thesis]. Hong Kong University of Science and Technology; 2014. [cited 2019 Dec 12]. Available from: https://doi.org/10.14711/thesis-b1334878 ; http://repository.ust.hk/ir/bitstream/1783.1-71826/1/th_redirect.html.

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

Council of Science Editors:

Bao Y. The explicit theta correspondence for reductive dual pairs (Sp(p,q),O*(4)). [Thesis]. Hong Kong University of Science and Technology; 2014. Available from: https://doi.org/10.14711/thesis-b1334878 ; http://repository.ust.hk/ir/bitstream/1783.1-71826/1/th_redirect.html

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

Hong Kong University of Science and Technology

2. Fan, Xiang. Explicit theta correspondence for the dual pairs (O(p,q),Sp(2n,R)) with p+q=4.

Degree: 2014, Hong Kong University of Science and Technology

URL: https://doi.org/10.14711/thesis-b1345731 ; http://repository.ust.hk/ir/bitstream/1783.1-71827/1/th_redirect.html

► In this thesis, we give a full and explicit description of the local theta correspondence for all the dual pairs (O(p,q), Sp(2n,R)) with p +… (more)

Subjects/Keywords: Functions, Theta; Representations of groups

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

APA (6^th Edition):

Fan, X. (2014). Explicit theta correspondence for the dual pairs (O(p,q),Sp(2n,R)) with p+q=4. (Thesis). Hong Kong University of Science and Technology. Retrieved from https://doi.org/10.14711/thesis-b1345731 ; http://repository.ust.hk/ir/bitstream/1783.1-71827/1/th_redirect.html

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

Chicago Manual of Style (16^th Edition):

Fan, Xiang. “Explicit theta correspondence for the dual pairs (O(p,q),Sp(2n,R)) with p+q=4.” 2014. Thesis, Hong Kong University of Science and Technology. Accessed December 12, 2019. https://doi.org/10.14711/thesis-b1345731 ; http://repository.ust.hk/ir/bitstream/1783.1-71827/1/th_redirect.html.

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

MLA Handbook (7^th Edition):

Fan, Xiang. “Explicit theta correspondence for the dual pairs (O(p,q),Sp(2n,R)) with p+q=4.” 2014. Web. 12 Dec 2019.

Vancouver:

Fan X. Explicit theta correspondence for the dual pairs (O(p,q),Sp(2n,R)) with p+q=4. [Internet] [Thesis]. Hong Kong University of Science and Technology; 2014. [cited 2019 Dec 12]. Available from: https://doi.org/10.14711/thesis-b1345731 ; http://repository.ust.hk/ir/bitstream/1783.1-71827/1/th_redirect.html.

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

Council of Science Editors:

Fan X. Explicit theta correspondence for the dual pairs (O(p,q),Sp(2n,R)) with p+q=4. [Thesis]. Hong Kong University of Science and Technology; 2014. Available from: https://doi.org/10.14711/thesis-b1345731 ; http://repository.ust.hk/ir/bitstream/1783.1-71827/1/th_redirect.html

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

University of Bradford

3. Evangelides, Pavlos. Analytic representations of quantum systems with Theta functions.

Degree: PhD, 2015, University of Bradford

URL: http://hdl.handle.net/10454/14366

► Quantum systems in a d-dimensional Hilbert space are considered, where the phase spase is Z(d) x Z(d). An analytic representation in a cell S in… (more)

Subjects/Keywords: Analytic functions; Theta functions; Bargmann functions; Finite quantum systems

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APA (6^th Edition):

Evangelides, P. (2015). Analytic representations of quantum systems with Theta functions. (Doctoral Dissertation). University of Bradford. Retrieved from http://hdl.handle.net/10454/14366

Chicago Manual of Style (16^th Edition):

Evangelides, Pavlos. “Analytic representations of quantum systems with Theta functions.” 2015. Doctoral Dissertation, University of Bradford. Accessed December 12, 2019. http://hdl.handle.net/10454/14366.

MLA Handbook (7^th Edition):

Evangelides, Pavlos. “Analytic representations of quantum systems with Theta functions.” 2015. Web. 12 Dec 2019.

Vancouver:

Evangelides P. Analytic representations of quantum systems with Theta functions. [Internet] [Doctoral dissertation]. University of Bradford; 2015. [cited 2019 Dec 12]. Available from: http://hdl.handle.net/10454/14366.

Council of Science Editors:

Evangelides P. Analytic representations of quantum systems with Theta functions. [Doctoral Dissertation]. University of Bradford; 2015. Available from: http://hdl.handle.net/10454/14366

Hong Kong University of Science and Technology

4. Du, Zhe. A description of discrete spectrum of (spin(10,2) x SL(2, R)) and singular theta correspondence.

Degree: 2009, Hong Kong University of Science and Technology

URL: https://doi.org/10.14711/thesis-b1044464 ; http://repository.ust.hk/ir/bitstream/1783.1-5989/1/th_redirect.html

► This thesis mainly comprises two parts. Both parts are related with Howe's dual reductive pair theory. Part I of the thesis gives a description of… (more)

▼ This thesis mainly comprises two parts. Both parts are related with Howe's dual reductive pair theory. Part I of the thesis gives a description of the full spectrum of the dual pair Spin(10, 2) x SL(2, R) in E7,3, the exception Lie group of type E7 with split real rank 3. As E7,3 is Hermitian symmetric, we have a detailed description of the minimal representation in [7]. Also, we know the correspondence of infinitesimal characters for dual pairs in [18]. The information of infinitesimal character and lowest K-types can nearly determine almost all representations occurring in the spectrum. Finally, we can see that the representations of E7,3 which occur in the spectrum are highest weight modules. Part II of the thesis is devoted to generalizing Borcherds result to the dual pair (U(1, 1), U(n, 1)). Let's briefly describe the content of each part. In Chapter 1, we will give some preparations work for Chapter 2 , and the embedding of the dual pair Spin(10, 2) x SL(2, R) into E7,3. Also, we will set some notations here. In Chapter 2, we focus on the description of the spectrum of Spin(10, 2) x SL(2, R), which is the restriction of the minimal representation of E7,3. In fact, we can view (Spin(10, 2), SL(2, R)) as a reductive dual pair inside E7,3. This description gives an explicit example of Howe correspondence. In Chapter 3, we will give some elementary results on theta correspondence and the Weil representation. In this chapter, we will mainly give some explanations on Borcherds' result. For example, the construction of the theta kernel, and what's more, the Fourier expansion developed by Borcherds. This Fourier expansion is similar to the Fourier-Jacobi expansion for Siegel modular forms on Sp(2, R). We can view it as a natural generalization of Saito-Kurokawa lifting to higher dimension. In Chapter 4, we will construct a theta function for the dual pair (U(1, 1), U(n, 1)) from the Schrodinger model. Then after setting some notations on the Hermitian symmetric space for U(n, 1), we will give a description of the Fourier-Jacobi expansion of the lifting.

Subjects/Keywords: Discrete groups; Functions, Theta; Representations of groups

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

APA (6^th Edition):

Du, Z. (2009). A description of discrete spectrum of (spin(10,2) x SL(2, R)) and singular theta correspondence. (Thesis). Hong Kong University of Science and Technology. Retrieved from https://doi.org/10.14711/thesis-b1044464 ; http://repository.ust.hk/ir/bitstream/1783.1-5989/1/th_redirect.html

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

Chicago Manual of Style (16^th Edition):

Du, Zhe. “A description of discrete spectrum of (spin(10,2) x SL(2, R)) and singular theta correspondence.” 2009. Thesis, Hong Kong University of Science and Technology. Accessed December 12, 2019. https://doi.org/10.14711/thesis-b1044464 ; http://repository.ust.hk/ir/bitstream/1783.1-5989/1/th_redirect.html.

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

MLA Handbook (7^th Edition):

Du, Zhe. “A description of discrete spectrum of (spin(10,2) x SL(2, R)) and singular theta correspondence.” 2009. Web. 12 Dec 2019.

Vancouver:

Du Z. A description of discrete spectrum of (spin(10,2) x SL(2, R)) and singular theta correspondence. [Internet] [Thesis]. Hong Kong University of Science and Technology; 2009. [cited 2019 Dec 12]. Available from: https://doi.org/10.14711/thesis-b1044464 ; http://repository.ust.hk/ir/bitstream/1783.1-5989/1/th_redirect.html.

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

Council of Science Editors:

Du Z. A description of discrete spectrum of (spin(10,2) x SL(2, R)) and singular theta correspondence. [Thesis]. Hong Kong University of Science and Technology; 2009. Available from: https://doi.org/10.14711/thesis-b1044464 ; http://repository.ust.hk/ir/bitstream/1783.1-5989/1/th_redirect.html

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

Hong Kong University of Science and Technology

5. Cong, Xuri. The dual pair (U(1),U(1,1)) over dyadic fields.

Degree: 2011, Hong Kong University of Science and Technology

URL: https://doi.org/10.14711/thesis-b1136737 ; http://repository.ust.hk/ir/bitstream/1783.1-7130/1/th_redirect.html

► It is well known that Howe's correspondence has been proved for reductive dual pair over local p-adic fields with p≠2. In this thesis, we examine… (more)

Subjects/Keywords: Functions, Theta; Functions of several complex variables; Representations of groups

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

APA (6^th Edition):

Cong, X. (2011). The dual pair (U(1),U(1,1)) over dyadic fields. (Thesis). Hong Kong University of Science and Technology. Retrieved from https://doi.org/10.14711/thesis-b1136737 ; http://repository.ust.hk/ir/bitstream/1783.1-7130/1/th_redirect.html

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

Chicago Manual of Style (16^th Edition):

Cong, Xuri. “The dual pair (U(1),U(1,1)) over dyadic fields.” 2011. Thesis, Hong Kong University of Science and Technology. Accessed December 12, 2019. https://doi.org/10.14711/thesis-b1136737 ; http://repository.ust.hk/ir/bitstream/1783.1-7130/1/th_redirect.html.

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

MLA Handbook (7^th Edition):

Cong, Xuri. “The dual pair (U(1),U(1,1)) over dyadic fields.” 2011. Web. 12 Dec 2019.

Vancouver:

Cong X. The dual pair (U(1),U(1,1)) over dyadic fields. [Internet] [Thesis]. Hong Kong University of Science and Technology; 2011. [cited 2019 Dec 12]. Available from: https://doi.org/10.14711/thesis-b1136737 ; http://repository.ust.hk/ir/bitstream/1783.1-7130/1/th_redirect.html.

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

Council of Science Editors:

Cong X. The dual pair (U(1),U(1,1)) over dyadic fields. [Thesis]. Hong Kong University of Science and Technology; 2011. Available from: https://doi.org/10.14711/thesis-b1136737 ; http://repository.ust.hk/ir/bitstream/1783.1-7130/1/th_redirect.html

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

6. NG SAY TIONG. Elliptic functions, theta functions and identities.

Degree: 2004, National University of Singapore

URL: http://scholarbank.nus.edu.sg/handle/10635/14317

Subjects/Keywords: elliptic functions; theta functions; identities

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APA (6^th Edition):

TIONG, N. S. (2004). Elliptic functions, theta functions and identities. (Thesis). National University of Singapore. Retrieved from http://scholarbank.nus.edu.sg/handle/10635/14317

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

Chicago Manual of Style (16^th Edition):

TIONG, NG SAY. “Elliptic functions, theta functions and identities.” 2004. Thesis, National University of Singapore. Accessed December 12, 2019. http://scholarbank.nus.edu.sg/handle/10635/14317.

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

MLA Handbook (7^th Edition):

TIONG, NG SAY. “Elliptic functions, theta functions and identities.” 2004. Web. 12 Dec 2019.

Vancouver:

TIONG NS. Elliptic functions, theta functions and identities. [Internet] [Thesis]. National University of Singapore; 2004. [cited 2019 Dec 12]. Available from: http://scholarbank.nus.edu.sg/handle/10635/14317.

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

Council of Science Editors:

TIONG NS. Elliptic functions, theta functions and identities. [Thesis]. National University of Singapore; 2004. Available from: http://scholarbank.nus.edu.sg/handle/10635/14317

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

Michigan State University

7. Yang, Jie. Elliptic functions, theta function, and submanifolds in space forms.

Degree: PhD, Department of Mathematics, 1997, Michigan State University

URL: http://etd.lib.msu.edu/islandora/object/etd:25456

Subjects/Keywords: Elliptic functions; Functions, Theta; Submanifolds

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

APA (6^th Edition):

Yang, J. (1997). Elliptic functions, theta function, and submanifolds in space forms. (Doctoral Dissertation). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:25456

Chicago Manual of Style (16^th Edition):

Yang, Jie. “Elliptic functions, theta function, and submanifolds in space forms.” 1997. Doctoral Dissertation, Michigan State University. Accessed December 12, 2019. http://etd.lib.msu.edu/islandora/object/etd:25456.

MLA Handbook (7^th Edition):

Yang, Jie. “Elliptic functions, theta function, and submanifolds in space forms.” 1997. Web. 12 Dec 2019.

Vancouver:

Yang J. Elliptic functions, theta function, and submanifolds in space forms. [Internet] [Doctoral dissertation]. Michigan State University; 1997. [cited 2019 Dec 12]. Available from: http://etd.lib.msu.edu/islandora/object/etd:25456.

Council of Science Editors:

Yang J. Elliptic functions, theta function, and submanifolds in space forms. [Doctoral Dissertation]. Michigan State University; 1997. Available from: http://etd.lib.msu.edu/islandora/object/etd:25456

Universidade do Rio Grande do Sul

8. Bagatini, Alessandro. Matrix representation for partitions and Mock Theta functions.

Degree: 2016, Universidade do Rio Grande do Sul

URL: http://hdl.handle.net/10183/150232

►

In this work, based on representations by matrices of two lines for some kind of partition (some already known and other new ones), we identify… (more)

▼

In this work, based on representations by matrices of two lines for some kind of partition (some already known and other new ones), we identify properties suggested by classifying them according to the sum of its second line. This sum always provides some properties of the related partition. If we consider unsigned versions of some Mock Theta Functions, its general term can be interpreted as generating function for some kind of partition with restrictions. To come back to the original coefficients, you can set a weight for each array and so add them to evaluate the coefficients. An analogous representation for partitions allows us to observe properties, again by classificating them according to the sum of its elements on the second row. This classification is made by means of tables created by mathematical software Maple, which suggest patterns, identities related to other known types of partitions and often, finding a closed formula to count them. Having established conjectured identities, all are proved by bijections between sets or counting methods.

Neste trabalho, com base em representações por matrizes de duas linhas para alguns tipos de partição (algumas já conhecidas e outras novas), identificamos propriedades sugeridas por classificá-las de acordo com a soma dos elementos de sua segunda linha. Esta soma sempre fornece alguma propriedade da partição relacionada. Se considerarmos versões sem sinal de algumas funções Mock Theta, seu termo geral pode ser interpretado como função geradora para algum tipo de partição com restrições. Para retornar aos coeficientes originais, é possível definir um peso para cada matriz e depois somá-las para contá-los. Uma representação análoga para essas partições nos permite observar propriedades sobre elas, novamente por meio de uma classificação referente à soma dos seu elementos da segunda linha. Esta seriação é feita por meio de tabelas criadas pelo software matemático Maple, as quais nos sugerem padrões e identidades relacionadas com outros tipos de partições conhecidas e, muitas vezes, encontrando uma fórmula fechada para contá-las. Tendo as conjecturas obtidas, elas são provadas por meio de bijeções entre conjuntos ou por contagem.

Advisors/Committee Members: Santos, Jose Plinio de Oliveira.

Subjects/Keywords: Partitions; Partições; Mock theta functions; Matrix representation; Young diagram; Bijection

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APA (6^th Edition):

Bagatini, A. (2016). Matrix representation for partitions and Mock Theta functions. (Thesis). Universidade do Rio Grande do Sul. Retrieved from http://hdl.handle.net/10183/150232

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

Chicago Manual of Style (16^th Edition):

Bagatini, Alessandro. “Matrix representation for partitions and Mock Theta functions.” 2016. Thesis, Universidade do Rio Grande do Sul. Accessed December 12, 2019. http://hdl.handle.net/10183/150232.

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

MLA Handbook (7^th Edition):

Bagatini, Alessandro. “Matrix representation for partitions and Mock Theta functions.” 2016. Web. 12 Dec 2019.

Vancouver:

Bagatini A. Matrix representation for partitions and Mock Theta functions. [Internet] [Thesis]. Universidade do Rio Grande do Sul; 2016. [cited 2019 Dec 12]. Available from: http://hdl.handle.net/10183/150232.

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

Council of Science Editors:

Bagatini A. Matrix representation for partitions and Mock Theta functions. [Thesis]. Universidade do Rio Grande do Sul; 2016. Available from: http://hdl.handle.net/10183/150232

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

Hong Kong University of Science and Technology

9. Yeung, Chi Yung. Local theta correspondence of reductive dual pair (U(1),U(1)).

Degree: 2004, Hong Kong University of Science and Technology

URL: https://doi.org/10.14711/thesis-b839598 ; http://repository.ust.hk/ir/bitstream/1783.1-5147/1/th_redirect.html

► In this thesis, the author reproves the result obtained by Moen, using a different model, lattice model, for the Weil representation. Using this model, the… (more)

Subjects/Keywords: Functions, Theta; Representations of groups

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

APA (6^th Edition):

Yeung, C. Y. (2004). Local theta correspondence of reductive dual pair (U(1),U(1)). (Thesis). Hong Kong University of Science and Technology. Retrieved from https://doi.org/10.14711/thesis-b839598 ; http://repository.ust.hk/ir/bitstream/1783.1-5147/1/th_redirect.html

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

Chicago Manual of Style (16^th Edition):

Yeung, Chi Yung. “Local theta correspondence of reductive dual pair (U(1),U(1)).” 2004. Thesis, Hong Kong University of Science and Technology. Accessed December 12, 2019. https://doi.org/10.14711/thesis-b839598 ; http://repository.ust.hk/ir/bitstream/1783.1-5147/1/th_redirect.html.

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

MLA Handbook (7^th Edition):

Yeung, Chi Yung. “Local theta correspondence of reductive dual pair (U(1),U(1)).” 2004. Web. 12 Dec 2019.

Vancouver:

Yeung CY. Local theta correspondence of reductive dual pair (U(1),U(1)). [Internet] [Thesis]. Hong Kong University of Science and Technology; 2004. [cited 2019 Dec 12]. Available from: https://doi.org/10.14711/thesis-b839598 ; http://repository.ust.hk/ir/bitstream/1783.1-5147/1/th_redirect.html.

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

Council of Science Editors:

Yeung CY. Local theta correspondence of reductive dual pair (U(1),U(1)). [Thesis]. Hong Kong University of Science and Technology; 2004. Available from: https://doi.org/10.14711/thesis-b839598 ; http://repository.ust.hk/ir/bitstream/1783.1-5147/1/th_redirect.html

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

University of Bradford

10. Olupitan, Tominiyi E. An analytic representation of weak mutually unbiased bases.

Degree: PhD, 2016, University of Bradford

URL: http://hdl.handle.net/10454/15904

► Quantum systems in the d-dimensional Hilbert space are considered. The mutually unbiased bases is a deep problem in this area. The problem of finding all… (more)

Subjects/Keywords: Finite quantum systems; Weak mutually unbiased bases; Finite geometry; Theta functions

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APA (6^th Edition):

Olupitan, T. E. (2016). An analytic representation of weak mutually unbiased bases. (Doctoral Dissertation). University of Bradford. Retrieved from http://hdl.handle.net/10454/15904

Chicago Manual of Style (16^th Edition):

Olupitan, Tominiyi E. “An analytic representation of weak mutually unbiased bases.” 2016. Doctoral Dissertation, University of Bradford. Accessed December 12, 2019. http://hdl.handle.net/10454/15904.

MLA Handbook (7^th Edition):

Olupitan, Tominiyi E. “An analytic representation of weak mutually unbiased bases.” 2016. Web. 12 Dec 2019.

Vancouver:

Olupitan TE. An analytic representation of weak mutually unbiased bases. [Internet] [Doctoral dissertation]. University of Bradford; 2016. [cited 2019 Dec 12]. Available from: http://hdl.handle.net/10454/15904.

Council of Science Editors:

Olupitan TE. An analytic representation of weak mutually unbiased bases. [Doctoral Dissertation]. University of Bradford; 2016. Available from: http://hdl.handle.net/10454/15904

Tulane University

11. Kesarwani, Aashita. Theory of the generalized modified Bessel function K_{z,w}(x) and 2-adic valuations of integer sequences.

Degree: 2017, Tulane University

URL: https://digitallibrary.tulane.edu/islandora/object/tulane:77514

►

Modular-type transformation formulas are the identities that are invariant under the transformation α → 1/α, and they can be represented as F (α) = F… (more)

▼

Modular-type transformation formulas are the identities that are invariant under the transformation α → 1/α, and they can be represented as F (α) = F (β) where α β = 1. We derive a new transformation formula of the form F (α, z, w) = F (β, z, iw) that is a one-variable generalization of the well-known Ramanujan-Guinand identity of the form F (α, z) = F (β, z) and a two-variable generalization of Koshliakov’s formula of the form F (α) = F (β) where α β = 1. The formula is generated by first finding an integral J that is comprised of an invariance function Z and evaluating the integral to give F (α, z, w) mentioned above. The modified Bessel function K z (x) appearing in Ramanujan-Guinand identity is generalized to a new function, denoted as K z,w (x), that yields a pair of functions reciprocal in the Koshliakov kernel, which in turn yields the invariance function Z and hence the integral J and the new formula. The special function K z,w (x), first defined as the inverse Mellin transform of a product of two gamma functions and two confluent hypergeometric functions, is shown to exhibit a rich theory as evidenced by a number of integral and series representations as well as a differential-difference equation. The second topic of the thesis is 2-adic valuations of integer sequences associated with quadratic polynomials of the form x 2 +a. The sequence {n 2 +a : n ∈ Z} contains numbers divisible by any power of 2 if and only if a is of the form 4 m (8l+7). Applying this result to the sequences derived from the sums of four or fewer squares when one or more of the squares are kept constant leads to interesting results, that also points to an inherent connection with the functions r k (n) that count the number of ways to represent n as sums of k integer squares. Another class of sequences studied is the shifted sequences of the polygonal numbers given by the quadratic formula, for which the most common examples are the triangular numbers and the squares.

1

Aashita Kesarwani

Advisors/Committee Members: Moll, Victor (Thesis advisor), School of Science & Engineering Mathematics (Degree granting institution).

Subjects/Keywords: Bessel functions; Theta transformation formula; Riemann zeta function

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

APA (6^th Edition):

Kesarwani, A. (2017). Theory of the generalized modified Bessel function K_{z,w}(x) and 2-adic valuations of integer sequences. (Thesis). Tulane University. Retrieved from https://digitallibrary.tulane.edu/islandora/object/tulane:77514

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

Chicago Manual of Style (16^th Edition):

Kesarwani, Aashita. “Theory of the generalized modified Bessel function K_{z,w}(x) and 2-adic valuations of integer sequences.” 2017. Thesis, Tulane University. Accessed December 12, 2019. https://digitallibrary.tulane.edu/islandora/object/tulane:77514.

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

MLA Handbook (7^th Edition):

Kesarwani, Aashita. “Theory of the generalized modified Bessel function K_{z,w}(x) and 2-adic valuations of integer sequences.” 2017. Web. 12 Dec 2019.

Vancouver:

Kesarwani A. Theory of the generalized modified Bessel function K_{z,w}(x) and 2-adic valuations of integer sequences. [Internet] [Thesis]. Tulane University; 2017. [cited 2019 Dec 12]. Available from: https://digitallibrary.tulane.edu/islandora/object/tulane:77514.

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

Council of Science Editors:

Kesarwani A. Theory of the generalized modified Bessel function K_{z,w}(x) and 2-adic valuations of integer sequences. [Thesis]. Tulane University; 2017. Available from: https://digitallibrary.tulane.edu/islandora/object/tulane:77514

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

University of Illinois – Urbana-Champaign

12. Schultz, Daniel. Cubic theta functions and identities for Appell's F1 function.

Degree: PhD, 0439, 2014, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/50667

► This thesis is centered around three topics: the theory of the cubic theta functions as functions of two analytic variables, cubic modular equations, and a… (more)

Subjects/Keywords: cubic theta functions; modular equations; appell hypergeometric; picard modular forms

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APA (6^th Edition):

Schultz, D. (2014). Cubic theta functions and identities for Appell's F1 function. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/50667

Chicago Manual of Style (16^th Edition):

Schultz, Daniel. “Cubic theta functions and identities for Appell's F1 function.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed December 12, 2019. http://hdl.handle.net/2142/50667.

MLA Handbook (7^th Edition):

Schultz, Daniel. “Cubic theta functions and identities for Appell's F1 function.” 2014. Web. 12 Dec 2019.

Vancouver:

Schultz D. Cubic theta functions and identities for Appell's F1 function. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2019 Dec 12]. Available from: http://hdl.handle.net/2142/50667.

Council of Science Editors:

Schultz D. Cubic theta functions and identities for Appell's F1 function. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/50667

University of Illinois – Urbana-Champaign

13. Yuttanan, Boonrod. Modular equations and Ramanujan's cubic and quartic theories of theta functions.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/29552

► In this thesis, we prove several identities involving Ramanujan's general theta function. In Chapter 2, we give proofs for new Ramanujan type modular equations discovered… (more)

Subjects/Keywords: modular equations; theta-functions; cubic theta-functions; eta-functions; partitions; colored partitions; continued fraction; power series expansion; periodicity of sign of coefficients; infinite series

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

APA (6^th Edition):

Yuttanan, B. (2012). Modular equations and Ramanujan's cubic and quartic theories of theta functions. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/29552

Chicago Manual of Style (16^th Edition):

Yuttanan, Boonrod. “Modular equations and Ramanujan's cubic and quartic theories of theta functions.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed December 12, 2019. http://hdl.handle.net/2142/29552.

MLA Handbook (7^th Edition):

Yuttanan, Boonrod. “Modular equations and Ramanujan's cubic and quartic theories of theta functions.” 2012. Web. 12 Dec 2019.

Vancouver:

Yuttanan B. Modular equations and Ramanujan's cubic and quartic theories of theta functions. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2019 Dec 12]. Available from: http://hdl.handle.net/2142/29552.

Council of Science Editors:

Yuttanan B. Modular equations and Ramanujan's cubic and quartic theories of theta functions. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/29552

14. Fouotsa, Emmanuel. Calcul des couplages et arithmétique des courbes elliptiques pour la cryptographie : Pairing computation and arithmetic of elliptic curves for cryptography.

Degree: Docteur es, Mathématiques fondamentales et applications, 2013, Rennes 1; Université européenne de Bretagne

URL: http://www.theses.fr/2013REN1S070

►

Alors qu'initialement utilisés pour résoudre le Problème du Logarithme Discret (DLP) dans le groupe de points d'une courbe elliptique, les couplages sont très à la… (more)

▼

Alors qu'initialement utilisés pour résoudre le Problème du Logarithme Discret (DLP) dans le groupe de points d'une courbe elliptique, les couplages sont très à la mode en cryptographie ces années car ils permettent de construire de nouveaux protocoles cryptographiques. Cependant, le calcul efficace du couplage dépend de l'arithmétique du modèle de courbe elliptique choisi et du corps sur lequel cette courbe est définie. Dans cette thèse, nous calculons le couplage sur deux modèles de Jacobi de courbes elliptiques puis nous introduisons et étudions l'arithmétique d'un nouveau modèle d'Ewards de courbe elliptique défini en toutes caractéristiques. Plus précisément, Nous utilisons l'interprétation géométrique de la loi de groupe sur l'intersection des quadriques de Jacobi pour obtenir pour la première fois dans la littérature, les formules explicites de la fonction de Miller pour le calcul du couplage de Tate sur cette courbe. Pour un calcul de couplage avec un degré de plongement pair, nous définissons la tordue quadratique pour obtenir des étapes de doublement et d'addition efficaces dans l'algorithme de Miller. Ensuite nous utilisons un isomorphisme entre la quartique spéciale de Jacobi Ed: Y²=dX⁴+Z⁴ et le modèle de Weierstrass pour obtenir la fonction de Miller nécessaire au calcul du couplage de Tate. Pour un degré de plongement divisible par 4, nous définissons la tordue d'ordre 4 de cette courbe pour obtenir un résultat meilleur du calcul du couplage de Tate par rapport aux courbes elliptiques sous forme de Weierstrass. Notre résultat améliore en même temps les derniers résultats obtenus sur cette courbe. Ce résultat est donc le meilleur connu à ce jour, à notre connaissance, pour le calcul du couplage de Tate sur les courbes possédant des tordues d'ordre 4. En 2006, Hess et al. introduisent le couplage Ate, qui est une version améliorée du couplage de Tate. Nous calculons ce couplage et ses variantes sur la même quartique. Nous y obtenons encore des résultats meilleurs. Notre troisième contribution est l'introduction d'un nouveau modèle d'Edwards de courbe elliptique d'équation 1+x²+y²+x²y²=Xxy. Ce modèle est ordinaire sur les corps de caractéristique 2 et nous montrons qu'il est birationnellement équivalent au modèle original d'Edwards x²+y²=c²(1+x²y²) en caractéristique différente de 2. Pour ce faire, nous utilisons la théorie des fonctions thêta et un modèle intermédiaire que nous appelons modèle thêta de niveau 4. Nous utilisons les relations de Riemann des fonctions thêta pour étudier l'arithmétique de ces deux courbes. Nous obtenons d'une part une loi de groupe complète, unifiée et en particulier compétitive en caractéristique 2 et d'autre part nous présentons les meilleures formules d'addition différentielle sur le modèle thêta de niveau 4.

While first used to solve the Discrete Logarithm Problem (DLP) in the group of points of elliptic curves, bilinear pairings are now useful to construct many public key protocols. The efficiency of pairings computation depends on the arithmetic of the model chosen…

Advisors/Committee Members: Duquesne, Sylvain (thesis director), Tonga, Marcel (thesis director).

Subjects/Keywords: Courbes elliptiques; Cryptographie; Couplages; Modèle de Jacobi; Modèled'Edwards; Fonctions theta; Elliptic curves; Cryptography; Pairings; Jacobi model; Edwards model; Theta functions

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

APA (6^th Edition):

Fouotsa, E. (2013). Calcul des couplages et arithmétique des courbes elliptiques pour la cryptographie : Pairing computation and arithmetic of elliptic curves for cryptography. (Doctoral Dissertation). Rennes 1; Université européenne de Bretagne. Retrieved from http://www.theses.fr/2013REN1S070

Chicago Manual of Style (16^th Edition):

Fouotsa, Emmanuel. “Calcul des couplages et arithmétique des courbes elliptiques pour la cryptographie : Pairing computation and arithmetic of elliptic curves for cryptography.” 2013. Doctoral Dissertation, Rennes 1; Université européenne de Bretagne. Accessed December 12, 2019. http://www.theses.fr/2013REN1S070.

MLA Handbook (7^th Edition):

Fouotsa, Emmanuel. “Calcul des couplages et arithmétique des courbes elliptiques pour la cryptographie : Pairing computation and arithmetic of elliptic curves for cryptography.” 2013. Web. 12 Dec 2019.

Vancouver:

Fouotsa E. Calcul des couplages et arithmétique des courbes elliptiques pour la cryptographie : Pairing computation and arithmetic of elliptic curves for cryptography. [Internet] [Doctoral dissertation]. Rennes 1; Université européenne de Bretagne; 2013. [cited 2019 Dec 12]. Available from: http://www.theses.fr/2013REN1S070.

Council of Science Editors:

Fouotsa E. Calcul des couplages et arithmétique des courbes elliptiques pour la cryptographie : Pairing computation and arithmetic of elliptic curves for cryptography. [Doctoral Dissertation]. Rennes 1; Université européenne de Bretagne; 2013. Available from: http://www.theses.fr/2013REN1S070

University of Vienna

15. Faulhuber, Markus. Extremal bounds of Gaussian Gabor Frames and properties of Jacobi's Theta Functions.

Degree: 2016, University of Vienna

URL: http://othes.univie.ac.at/45666/

►

In dieser Arbeit werden scharfe Schranken von Gabor Frames mit einem Gauss Fenster studiert. Es wird untersucht, wie sich die Frame Schranken in Abhängigkeit des… (more)

Subjects/Keywords: 31.35 Harmonische Analyse; 31.40 Analysis: Allgemeines; Frame Schranken / Gabor Frames / Jacobi Theta Funktionen; Frame Bounds / Gabor Frames / Jacobi Theta Functions

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

APA (6^th Edition):

Faulhuber, M. (2016). Extremal bounds of Gaussian Gabor Frames and properties of Jacobi's Theta Functions. (Thesis). University of Vienna. Retrieved from http://othes.univie.ac.at/45666/

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

Chicago Manual of Style (16^th Edition):

Faulhuber, Markus. “Extremal bounds of Gaussian Gabor Frames and properties of Jacobi's Theta Functions.” 2016. Thesis, University of Vienna. Accessed December 12, 2019. http://othes.univie.ac.at/45666/.

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

MLA Handbook (7^th Edition):

Faulhuber, Markus. “Extremal bounds of Gaussian Gabor Frames and properties of Jacobi's Theta Functions.” 2016. Web. 12 Dec 2019.

Vancouver:

Faulhuber M. Extremal bounds of Gaussian Gabor Frames and properties of Jacobi's Theta Functions. [Internet] [Thesis]. University of Vienna; 2016. [cited 2019 Dec 12]. Available from: http://othes.univie.ac.at/45666/.

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

Council of Science Editors:

Faulhuber M. Extremal bounds of Gaussian Gabor Frames and properties of Jacobi's Theta Functions. [Thesis]. University of Vienna; 2016. Available from: http://othes.univie.ac.at/45666/

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

16. Nath, Kallol. Contributions to t core partitions for some small t by using ramanujans theta functions; -.

Degree: Mathematical Science, 2013, Tezpur University

URL: http://shodhganga.inflibnet.ac.in/handle/10603/41198

Abstract Available

Bibliography p.98-103

Advisors/Committee Members: Baruah, Nayandeep Deka.

Subjects/Keywords: core partitions; sing ramanujans; theta functions

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APA (6^th Edition):

Nath, K. (2013). Contributions to t core partitions for some small t by using ramanujans theta functions; -. (Thesis). Tezpur University. Retrieved from http://shodhganga.inflibnet.ac.in/handle/10603/41198

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

Chicago Manual of Style (16^th Edition):

Nath, Kallol. “Contributions to t core partitions for some small t by using ramanujans theta functions; -.” 2013. Thesis, Tezpur University. Accessed December 12, 2019. http://shodhganga.inflibnet.ac.in/handle/10603/41198.

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

MLA Handbook (7^th Edition):

Nath, Kallol. “Contributions to t core partitions for some small t by using ramanujans theta functions; -.” 2013. Web. 12 Dec 2019.

Vancouver:

Nath K. Contributions to t core partitions for some small t by using ramanujans theta functions; -. [Internet] [Thesis]. Tezpur University; 2013. [cited 2019 Dec 12]. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/41198.

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

Council of Science Editors:

Nath K. Contributions to t core partitions for some small t by using ramanujans theta functions; -. [Thesis]. Tezpur University; 2013. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/41198

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

Universidade do Rio Grande do Sul

17. Matte, Marília Luiza. Matrix representations for integer partitions : some consequences and a new approach.

Degree: 2018, Universidade do Rio Grande do Sul

URL: http://hdl.handle.net/10183/178603

► O presente trabalho dedica-se ao estudo de algumas consequências da representação matricial para conjuntos de partições de inteiros e funções mock theta. Na primeira parte… (more)

Subjects/Keywords: Integer Partitions; Particao de inteiros; Partições; Matrix Representation; Partition Identities; Mock Theta Functions

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APA (6^th Edition):

Matte, M. L. (2018). Matrix representations for integer partitions : some consequences and a new approach. (Thesis). Universidade do Rio Grande do Sul. Retrieved from http://hdl.handle.net/10183/178603

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

Chicago Manual of Style (16^th Edition):

Matte, Marília Luiza. “Matrix representations for integer partitions : some consequences and a new approach.” 2018. Thesis, Universidade do Rio Grande do Sul. Accessed December 12, 2019. http://hdl.handle.net/10183/178603.

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

MLA Handbook (7^th Edition):

Matte, Marília Luiza. “Matrix representations for integer partitions : some consequences and a new approach.” 2018. Web. 12 Dec 2019.

Vancouver:

Matte ML. Matrix representations for integer partitions : some consequences and a new approach. [Internet] [Thesis]. Universidade do Rio Grande do Sul; 2018. [cited 2019 Dec 12]. Available from: http://hdl.handle.net/10183/178603.

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

Council of Science Editors:

Matte ML. Matrix representations for integer partitions : some consequences and a new approach. [Thesis]. Universidade do Rio Grande do Sul; 2018. Available from: http://hdl.handle.net/10183/178603

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

University of Illinois – Urbana-Champaign

18. Kim, Byung Chan. Arithmetic of partition functions and q-combinatorics.

Degree: PhD, 0439, 2010, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/15588

► Integer partitions play important roles in diverse areas of mathematics such as q-series, the theory of modular forms, representation theory, symmetric functions and mathematical physics.… (more)

Subjects/Keywords: Partitions; Partition congruences; q-series; Modular forms; Combinatorial proof; Mock theta functions

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APA (6^th Edition):

Kim, B. C. (2010). Arithmetic of partition functions and q-combinatorics. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/15588

Chicago Manual of Style (16^th Edition):

Kim, Byung Chan. “Arithmetic of partition functions and q-combinatorics.” 2010. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed December 12, 2019. http://hdl.handle.net/2142/15588.

MLA Handbook (7^th Edition):

Kim, Byung Chan. “Arithmetic of partition functions and q-combinatorics.” 2010. Web. 12 Dec 2019.

Vancouver:

Kim BC. Arithmetic of partition functions and q-combinatorics. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2010. [cited 2019 Dec 12]. Available from: http://hdl.handle.net/2142/15588.

Council of Science Editors:

Kim BC. Arithmetic of partition functions and q-combinatorics. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2010. Available from: http://hdl.handle.net/2142/15588

University of Texas – Austin

19. Pacetti, Ariel Martín. A formula for the central value of certain Hecke L-functions.

Degree: PhD, Mathematics, 2003, University of Texas – Austin

URL: http://hdl.handle.net/2152/830

► Let N ≡ 1 mod 4 be the negative of a prime, K = Q( √ N) and OK its ring of integers. Let D… (more)

Subjects/Keywords: Functions, Theta; Forms, Modular; Hecke operators

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

APA (6^th Edition):

Pacetti, A. M. (2003). A formula for the central value of certain Hecke L-functions. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/830

Chicago Manual of Style (16^th Edition):

Pacetti, Ariel Martín. “A formula for the central value of certain Hecke L-functions.” 2003. Doctoral Dissertation, University of Texas – Austin. Accessed December 12, 2019. http://hdl.handle.net/2152/830.

MLA Handbook (7^th Edition):

Pacetti, Ariel Martín. “A formula for the central value of certain Hecke L-functions.” 2003. Web. 12 Dec 2019.

Vancouver:

Pacetti AM. A formula for the central value of certain Hecke L-functions. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2003. [cited 2019 Dec 12]. Available from: http://hdl.handle.net/2152/830.

Council of Science Editors:

Pacetti AM. A formula for the central value of certain Hecke L-functions. [Doctoral Dissertation]. University of Texas – Austin; 2003. Available from: http://hdl.handle.net/2152/830

University of Michigan

20. Zhang, Ming. Quantum K-Theory with Level Structure.

Degree: PhD, Mathematics, 2019, University of Michigan

URL: http://hdl.handle.net/2027.42/151499

► Given a smooth, complex projective variety X, one can associate to it numerical invariants by taking holomorphic Euler characteristics of natural vector bundles on the… (more)

▼ Given a smooth, complex projective variety X, one can associate to it numerical invariants by taking holomorphic Euler characteristics of natural vector bundles on the moduli spaces of stable maps to X. The study of these invariants is called quantum K-theory. Since K-theory is closely related to representation theory, it is natural to revisit quantum K-theory from the representation theoretic point of view. One of the important concepts in representation theory is level. In this thesis, we introduce the notion of level in quasimap theory and refer to it as the level structure. This thesis consists of two parts. In the first part, we define level structures in quasimap theory as certain determinant line bundles over moduli spaces of quasimaps. By twisting with these determinant line bundles, we define K-theoretic quasimap invariants with level structure. An important case of this construction is quantum K-theory with level structure. We study the basic properties of level structures and show that quantum K-theory with level structure satisfies the same axioms as the ordinary, i.e., Givental-Lee's, quantum K-theory. In the genus-0 case, the invariants are encoded in an important generating series: the J-function. We characterize the values of the J-function in quantum K-theory with level structure. As an application of this characterization, we prove a mirror theorem for toric varieties. One surprising finding is that the mirrors of some of the simplest examples are Ramanujan's mock theta functions. In the second part, we study the Verlinde/Grassmannian correspondence, which is a K-theoretic generalization of Witten's result. It relates the Verlinde algebra, a representation theoretic object, with the quantum K-invariants of the Grassmannian with level structure. To prove this correspondence, an important observation is that the Verlinde invariants and quantum K-invariants of the Grassmannian can be defined using the same gauged linear sigma model but with different stability conditions. In this thesis, we study the delta-stability condition. In particular, we construct the moduli spaces of delta-stable parabolic N-pairs and prove that they are equipped with canonical perfect obstruction theories. Using virtual structure sheaves, we define Verlinde type invariants over these moduli spaces and prove that they do not change when we vary the stability parameter delta. Advisors/Committee Members: Ruan, Yongbin (committee member), Pando Zayas, Leopoldo A (committee member), Burns Jr, Daniel M (committee member), Fulton, William (committee member).

Subjects/Keywords: Quantum K-theory; Level structure; Mock theta functions; Verlinde algebra; Mathematics; Science

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APA (6^th Edition):

Zhang, M. (2019). Quantum K-Theory with Level Structure. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/151499

Chicago Manual of Style (16^th Edition):

Zhang, Ming. “Quantum K-Theory with Level Structure.” 2019. Doctoral Dissertation, University of Michigan. Accessed December 12, 2019. http://hdl.handle.net/2027.42/151499.

MLA Handbook (7^th Edition):

Zhang, Ming. “Quantum K-Theory with Level Structure.” 2019. Web. 12 Dec 2019.

Vancouver:

Zhang M. Quantum K-Theory with Level Structure. [Internet] [Doctoral dissertation]. University of Michigan; 2019. [cited 2019 Dec 12]. Available from: http://hdl.handle.net/2027.42/151499.

Council of Science Editors:

Zhang M. Quantum K-Theory with Level Structure. [Doctoral Dissertation]. University of Michigan; 2019. Available from: http://hdl.handle.net/2027.42/151499

Northeastern University

21. Bolognese, Barbara. Two results on divisors on moduli spaces of sheaves on algebraic surfaces: generic Strange Duality on abelian surfaces and Nef cones of Hilbert schemes of points on surfaces with irregularity zero.

Degree: PhD, Department of Mathematics, 2016, Northeastern University

URL: http://hdl.handle.net/2047/D20211213

► In the first part of this thesis, we consider a special version of Le Potier's strange duality conjecture for sheaves over abelian surfaces, after other… (more)

Subjects/Keywords: Abelian surfaces; Bridgeland stability; moduli spaces; Nef cone; strange duality; Theta divisors; Sheaf theory; Moduli theory; Surfaces, Algebraic; Abelian varieties; Cone; Stability; Functions, Theta

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

APA (6^th Edition):

Bolognese, B. (2016). Two results on divisors on moduli spaces of sheaves on algebraic surfaces: generic Strange Duality on abelian surfaces and Nef cones of Hilbert schemes of points on surfaces with irregularity zero. (Doctoral Dissertation). Northeastern University. Retrieved from http://hdl.handle.net/2047/D20211213

Chicago Manual of Style (16^th Edition):

Bolognese, Barbara. “Two results on divisors on moduli spaces of sheaves on algebraic surfaces: generic Strange Duality on abelian surfaces and Nef cones of Hilbert schemes of points on surfaces with irregularity zero.” 2016. Doctoral Dissertation, Northeastern University. Accessed December 12, 2019. http://hdl.handle.net/2047/D20211213.

MLA Handbook (7^th Edition):

Bolognese, Barbara. “Two results on divisors on moduli spaces of sheaves on algebraic surfaces: generic Strange Duality on abelian surfaces and Nef cones of Hilbert schemes of points on surfaces with irregularity zero.” 2016. Web. 12 Dec 2019.

Vancouver:

Bolognese B. Two results on divisors on moduli spaces of sheaves on algebraic surfaces: generic Strange Duality on abelian surfaces and Nef cones of Hilbert schemes of points on surfaces with irregularity zero. [Internet] [Doctoral dissertation]. Northeastern University; 2016. [cited 2019 Dec 12]. Available from: http://hdl.handle.net/2047/D20211213.

Council of Science Editors:

Bolognese B. Two results on divisors on moduli spaces of sheaves on algebraic surfaces: generic Strange Duality on abelian surfaces and Nef cones of Hilbert schemes of points on surfaces with irregularity zero. [Doctoral Dissertation]. Northeastern University; 2016. Available from: http://hdl.handle.net/2047/D20211213

University of Colorado

22. Keyes, David Parker. Analytic Proofs of Certain MacWilliams Identities.

Degree: PhD, Mathematics, 2011, University of Colorado

URL: http://scholar.colorado.edu/math_gradetds/10

Subjects/Keywords: Codes; MacWilliams Identities; Modular Forms; Theta Functions; Mathematics

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APA (6^th Edition):

Keyes, D. P. (2011). Analytic Proofs of Certain MacWilliams Identities. (Doctoral Dissertation). University of Colorado. Retrieved from http://scholar.colorado.edu/math_gradetds/10

Chicago Manual of Style (16^th Edition):

Keyes, David Parker. “Analytic Proofs of Certain MacWilliams Identities.” 2011. Doctoral Dissertation, University of Colorado. Accessed December 12, 2019. http://scholar.colorado.edu/math_gradetds/10.

MLA Handbook (7^th Edition):

Keyes, David Parker. “Analytic Proofs of Certain MacWilliams Identities.” 2011. Web. 12 Dec 2019.

Vancouver:

Keyes DP. Analytic Proofs of Certain MacWilliams Identities. [Internet] [Doctoral dissertation]. University of Colorado; 2011. [cited 2019 Dec 12]. Available from: http://scholar.colorado.edu/math_gradetds/10.

Council of Science Editors:

Keyes DP. Analytic Proofs of Certain MacWilliams Identities. [Doctoral Dissertation]. University of Colorado; 2011. Available from: http://scholar.colorado.edu/math_gradetds/10

23. Jaber, Carine. Algorithmic approaches to Siegel's fundamental domain : Approches algorithmiques du domaine fondamental de Siegel.

Degree: Docteur es, Mathématiques, 2017, Bourgogne Franche-Comté

URL: http://www.theses.fr/2017UBFCK006

►

Siegel détermina un domaine fondamental à l'aide de la réduction de Minkowski des formes quadratiques. Il donna tous les détails concernant ce domaine pour le… (more)

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Siegel détermina un domaine fondamental à l'aide de la réduction de Minkowski des formes quadratiques. Il donna tous les détails concernant ce domaine pour le genre 1. C'est la détermination du domaine fondamental de Minkowski présentée comme deuxième condition et la condition maximal height présentée comme troisième condition, qui empêchent la précision exacte de ce domaine pour le cas général. Les derniers résultats ont été obtenus par Gottschling pour le genre 2 en 1959. Elle est depuis restée inexplorée et mal comprise notamment les différents domaines de Minkowski. Afin d'identifier ce domaine fondamental pour le genre 3, nous présentons des résultats concernant sa troisième condition. Chaque fonction abélienne peut être écrite en termes de fonctions rationnelles des fonctions thêta et de leurs dérivées. Cela permet l'expression de la solution des systèmes intégrables en fonction des fonctions thêta. Ces solutions sont pertinentes dans la description de surfaces de vagues d'eau, de l'optique non linéaire. Deconinck et Van Hoeij ont éveloppé et mis en oeuvre des algorithmes pour construire la matrice de Riemann et Deconinck et al. ont développé le calcul des fonctions thêta correspondantes. Deconinck et al. ont utilisé l'algorithme de Siegel pour atteindre approximativement le domaine fondamental de Siegel et ont adopté l'algorithme LLL pour trouver le vecteur le plus court. Alors que nous utilisons ici un nouvel algorithme de réduction de Minkowski jusqu'à dimension 5 et une détermination exacte du vecteur le plus court pour des dimensions supérieures.

Siegel determined a fundamental domain using the Minkowski reduction of quadratic forms. He gave all the details concerning this domain for genus 1. It is the determination of the Minkowski fundamental domain presented as the second condition and the maximal height condition, presented as the third condition, which prevents the exact determination of this domain for the general case. The latest results were obtained by Gottschling for the genus 2 in 1959. It has since remained unexplored and poorly understood, in particular the different regions of Minkowski reduction. In order to identify Siegel's fundamental domain for genus 3, we present some results concerning the third condition of this domain. Every abelian function can be written in terms of rational functions of theta functions and their derivatives. This allows the expression of solutions of integrable systems in terms of theta functions. Such solutions are relevant in the description of surface water waves, non linear optics. Because of these applications, Deconinck and Van Hoeij have developed and implemented al-gorithms for computing the Riemann matrix and Deconinck et al. have developed the computation of the corresponding theta functions. Deconinck et al. have used Siegel's algorithm to approximately reach the Siegel fundamental domain and have adopted the LLL reduction algorithm to nd the shortest lattice vector. However, we opt here to use a Minkowski algorithmup to dimension 5 and an exact…

Advisors/Committee Members: Klein, Christian (thesis director).

Subjects/Keywords: Réduction de Minkowski; Domaine fondamental de Siegel; Fonctions thêta; Minkowski ‘s reduction; Siegel’s fundamental domain; Theta functions; 510

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APA (6^th Edition):

Jaber, C. (2017). Algorithmic approaches to Siegel's fundamental domain : Approches algorithmiques du domaine fondamental de Siegel. (Doctoral Dissertation). Bourgogne Franche-Comté. Retrieved from http://www.theses.fr/2017UBFCK006

Chicago Manual of Style (16^th Edition):

Jaber, Carine. “Algorithmic approaches to Siegel's fundamental domain : Approches algorithmiques du domaine fondamental de Siegel.” 2017. Doctoral Dissertation, Bourgogne Franche-Comté. Accessed December 12, 2019. http://www.theses.fr/2017UBFCK006.

MLA Handbook (7^th Edition):

Jaber, Carine. “Algorithmic approaches to Siegel's fundamental domain : Approches algorithmiques du domaine fondamental de Siegel.” 2017. Web. 12 Dec 2019.

Vancouver:

Jaber C. Algorithmic approaches to Siegel's fundamental domain : Approches algorithmiques du domaine fondamental de Siegel. [Internet] [Doctoral dissertation]. Bourgogne Franche-Comté; 2017. [cited 2019 Dec 12]. Available from: http://www.theses.fr/2017UBFCK006.

Council of Science Editors:

Jaber C. Algorithmic approaches to Siegel's fundamental domain : Approches algorithmiques du domaine fondamental de Siegel. [Doctoral Dissertation]. Bourgogne Franche-Comté; 2017. Available from: http://www.theses.fr/2017UBFCK006

24. Munaro, Andrea. Sur quelques invariants classiques et nouveaux des hypergraphes : On some classical and new hypergraph invariants.

Degree: Docteur es, Informatique et mathématiques appliquées, 2016, Grenoble Alpes

URL: http://www.theses.fr/2016GREAM072

► Dans cette thèse, nous considérons plusieurs paramètres des hypergraphes et nous étudions si les restrictions aux sous-classes des hypergraphes permettent d’obtenir des propriétés combinatoires et… (more)

▼ Dans cette thèse, nous considérons plusieurs paramètres des hypergraphes et nous étudions si les restrictions aux sous-classes des hypergraphes permettent d’obtenir des propriétés combinatoires et algorithmiques souhaitables. La plupart des paramètres que nous prenons en compte sont des instances spéciales des packings et transversals des hypergraphes.Dans la première partie, nous allons nous concentrer sur les line graphs des graphes subcubiques sans triangle et nous allons démontrer que pour tous ces graphes il y a un independent set de taille au moins 3|V(G)|/10 et cette borne est optimale. Conséquence immédiate: nous obtenons une borne inférieure optimale pour la taille d’un couplage maximum dans les graphes subcubiques sans triangle. De plus, nous montrons plusieurs résultats algorithmiques liés au FEEDBACK VERTEX SET, HAMILTONIAN CYCLE et HAMILTONIAN PATH quand restreints aux line graphs des graphes subcubiques sans triangle.Puis nous examinons trois hypergraphes ayant la propriété d’Erdős-Pósa et nous cherchons à déterminer les fonctions limites optimales. Tout d’abord, nous apportons une fonction theta-bounding pour la classe des graphes subcubiques et nous étudions CLIQUE COVER: en répondant à une question de Cerioli et al., nous montrons qu’il admet un PTAS pour les graphes planaires. Par la suite, nous nous intéressons à la Conjecture de Tuza et nous montrons que la constante 2 peut être améliorée pour les graphes avec arêtes contenues dans au maximum quatre triangles et pour les graphes sans certains odd-wheels. Enfin, nous nous concentrons sur la Conjecture de Jones: nous la démontrons dans le cas des graphes sans griffes avec degré maximal 4 et nous faisons quelques observations dans le cas des graphes subcubiques.Nous étudions ensuite la VC-dimension de certains hypergraphes résultants des graphes. En particulier, nous considérons l’hypergraphe sur l’ensemble des sommets d’un certain graphe qui est induit par la famille de ses sous-graphes k-connexes. En généralisant les résultats de Kranakis et al., nous fournissons des bornes supérieures et inférieures optimales pour la VC-dimension et nous montrons que son calcul est NP-complet, pour chacun k > 0. Enfin, nous démontrons que ce problème (dans le cas k = 1) et le problème étroitement lié CONNECTED DOMINATING SET sont soit solvables en temps polynomial ou NP-complet, quand restreints aux classes de graphes obtenues en interdisant un seul sous-graphe induit.Dans la partie finale de cette thèse, nous nous attaquons aux meta-questions suivantes: Quand est-ce qu’un certain problème “difficile” de graphe devient “facile”?; Existe-t-il des frontières séparant des instances “faciles” et “difficiles”? Afin de répondre à ces questions, dans le cas des classes héréditaires, Alekseev a introduit la notion de boundary class pour un problème NP-difficile et a montré qu’un problème Pi est NP-difficile pour une classe héréditaire X finiment défini si et seulement si X contient un boundary class pour Pi. Nouscontinuons la recherche des boundary classes pour les… Advisors/Committee Members: Sebő, András (thesis director), Stehlík, Matěj (thesis director).

Subjects/Keywords: Graphes; Paramètre des hypergraphes; NP-complétude; Line graphs; Hypergraph parameters; Boundary classes; VC-dimension; NP-completeness; Theta-bounding functions; 004

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

APA (6^th Edition):

Munaro, A. (2016). Sur quelques invariants classiques et nouveaux des hypergraphes : On some classical and new hypergraph invariants. (Doctoral Dissertation). Grenoble Alpes. Retrieved from http://www.theses.fr/2016GREAM072

Chicago Manual of Style (16^th Edition):

Munaro, Andrea. “Sur quelques invariants classiques et nouveaux des hypergraphes : On some classical and new hypergraph invariants.” 2016. Doctoral Dissertation, Grenoble Alpes. Accessed December 12, 2019. http://www.theses.fr/2016GREAM072.

MLA Handbook (7^th Edition):

Munaro, Andrea. “Sur quelques invariants classiques et nouveaux des hypergraphes : On some classical and new hypergraph invariants.” 2016. Web. 12 Dec 2019.

Vancouver:

Munaro A. Sur quelques invariants classiques et nouveaux des hypergraphes : On some classical and new hypergraph invariants. [Internet] [Doctoral dissertation]. Grenoble Alpes; 2016. [cited 2019 Dec 12]. Available from: http://www.theses.fr/2016GREAM072.

Council of Science Editors:

Munaro A. Sur quelques invariants classiques et nouveaux des hypergraphes : On some classical and new hypergraph invariants. [Doctoral Dissertation]. Grenoble Alpes; 2016. Available from: http://www.theses.fr/2016GREAM072

25. Robert, Damien. Fonction thêta et applications à la cryptographie : Theta functions and cryptographic applications : theta functions and applications in cryptography.

Degree: Docteur es, Informatique, 2010, Université Henri Poincaré – Nancy I

URL: http://www.theses.fr/2010NAN10037

►

Le logarithme discret sur les courbes elliptiques fournit la panoplie standard de la cryptographie à clé publique: chiffrement asymétrique, signature, authentification. Son extension à des… (more)

▼

Le logarithme discret sur les courbes elliptiques fournit la panoplie standard de la cryptographie à clé publique: chiffrement asymétrique, signature, authentification. Son extension à des courbes hyperelliptiques de genre supérieur se heurte à la difficulté de construire de telles courbes qui soient sécurisées. Dans cette thèse nous utilisons la théorie des fonctions thêta développée par Mumford pour construire des algorithmes efficaces pour manipuler les variétés abéliennes. En particulier nous donnons une généralisation complète des formules de Vélu sur les courbes elliptiques pour le calcul d'isogénie sur des variétés abéliennes. Nous donnons également un nouvel algorithme pour le calcul efficace de couplage sur les variétés abéliennes en utilisant les coordonnées thêta. Enfin, nous présentons une méthode de compression des coordonnées pour améliorer l'arithmétique sur les coordonnées thêta de grand niveau. Ces applications découlent d'une analyse fine des formules d'addition sur les fonctions thêta. Si les résultats de cette thèse sont valables pour toute variété abélienne, pour les applications nous nous concentrons surtout sur les jacobienne de courbes hyperelliptiques de genre~2, qui est le cas le plus significatif cryptographiquement.

The discrete logarithm on elliptic curves give the standard protocols in public key cryptography: asymmetric encryption, signatures, ero-knowledge authentification. To extends the discrete logarithm to hyperelliptic curves of higher genus we need efficient methods to generate secure curves. The aim of this thesis is to give new algorithms to compute with abelian varieties. For this we use the theory of algebraic theta functions in the framework of Mumford. In particular, we give a full generalization of Vélu's formulas for the computation of isogenies on abelian varieties. We also give a new algorithm for the computation of pairings using theta coordinates. Finally we present a point compression method to manipulate These applications follow from the analysis of Riemann relations on theta functions for the addition law. If the results of this thesis are valid for any abelian variety, for the applications a special emphasis is given to Jacobians of hyperelliptic genus~2 curves, since they are the most significantly relevant case in cryptography.

Advisors/Committee Members: Hanrot, Guillaume (thesis director).

Subjects/Keywords: Cryptographie; Courbes hyperelliptiques; Variétés abéliennes; Isogénies; Couplage; Fonctions thêta; Cryptography; Hyperelliptic curves; Abelian varieties; Isogenies; Pairing; Theta functions

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APA (6^th Edition):

Robert, D. (2010). Fonction thêta et applications à la cryptographie : Theta functions and cryptographic applications : theta functions and applications in cryptography. (Doctoral Dissertation). Université Henri Poincaré – Nancy I. Retrieved from http://www.theses.fr/2010NAN10037

Chicago Manual of Style (16^th Edition):

Robert, Damien. “Fonction thêta et applications à la cryptographie : Theta functions and cryptographic applications : theta functions and applications in cryptography.” 2010. Doctoral Dissertation, Université Henri Poincaré – Nancy I. Accessed December 12, 2019. http://www.theses.fr/2010NAN10037.

MLA Handbook (7^th Edition):

Robert, Damien. “Fonction thêta et applications à la cryptographie : Theta functions and cryptographic applications : theta functions and applications in cryptography.” 2010. Web. 12 Dec 2019.

Vancouver:

Robert D. Fonction thêta et applications à la cryptographie : Theta functions and cryptographic applications : theta functions and applications in cryptography. [Internet] [Doctoral dissertation]. Université Henri Poincaré – Nancy I; 2010. [cited 2019 Dec 12]. Available from: http://www.theses.fr/2010NAN10037.

Council of Science Editors:

Robert D. Fonction thêta et applications à la cryptographie : Theta functions and cryptographic applications : theta functions and applications in cryptography. [Doctoral Dissertation]. Université Henri Poincaré – Nancy I; 2010. Available from: http://www.theses.fr/2010NAN10037

Universiteit Utrecht

26. Wasserman, T.A. Orbifold Conformal Field Theory and One-Loop Self-Energy in the $S_N\R^D$ Orbifold Sigma Model.

Degree: 2012, Universiteit Utrecht

URL: http://dspace.library.uu.nl:8080/handle/1874/253427

► In this thesis both mathematical and physical aspects of orbifold conformal field theory are described. We present a set-up to do a one-loop self-energy computation… (more)

Subjects/Keywords: Conformal field theory; string theory; vertex operator algebras; twist fields; twisted vertex algebras; covering maps; orbifold conformal field theory; vertex algebras; conformal vertex algebras; riemann surfaces; theta functions

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

APA (6^th Edition):

Wasserman, T. A. (2012). Orbifold Conformal Field Theory and One-Loop Self-Energy in the $S_N\R^D$ Orbifold Sigma Model. (Masters Thesis). Universiteit Utrecht. Retrieved from http://dspace.library.uu.nl:8080/handle/1874/253427

Chicago Manual of Style (16^th Edition):

Wasserman, T A. “Orbifold Conformal Field Theory and One-Loop Self-Energy in the $S_N\R^D$ Orbifold Sigma Model.” 2012. Masters Thesis, Universiteit Utrecht. Accessed December 12, 2019. http://dspace.library.uu.nl:8080/handle/1874/253427.

MLA Handbook (7^th Edition):

Wasserman, T A. “Orbifold Conformal Field Theory and One-Loop Self-Energy in the $S_N\R^D$ Orbifold Sigma Model.” 2012. Web. 12 Dec 2019.

Vancouver:

Wasserman TA. Orbifold Conformal Field Theory and One-Loop Self-Energy in the $S_N\R^D$ Orbifold Sigma Model. [Internet] [Masters thesis]. Universiteit Utrecht; 2012. [cited 2019 Dec 12]. Available from: http://dspace.library.uu.nl:8080/handle/1874/253427.

Council of Science Editors:

Wasserman TA. Orbifold Conformal Field Theory and One-Loop Self-Energy in the $S_N\R^D$ Orbifold Sigma Model. [Masters Thesis]. Universiteit Utrecht; 2012. Available from: http://dspace.library.uu.nl:8080/handle/1874/253427

Texas A&M University

27. Wanderley De Holanda, Rafael. Material Balance Reservoir Models Derived from Production Data.

Degree: PhD, Petroleum Engineering, 2019, Texas A&M University

URL: http://hdl.handle.net/1969.1/185018

► Rate measurements are the most available data gathered throughout the production life of a field, and essential to understand reservoir dynamics. In order to gain… (more)

▼ Rate measurements are the most available data gathered throughout the production life of a field, and essential to understand reservoir dynamics. In order to gain knowledge quickly from such data for a massive number of wells, it is important to develop simple reservoir models capable of history matching and predicting performance using rate measurements, but also incorporating other types of data (e.g. bottomhole pressures, well locations, completion status), as available. Even in simplified reservoir models, material balance is a necessary assumption because reservoirs are limited resources of petroleum. In this context, capacitance resistance models (CRM’s) comprise a family of material balance reservoir models that have been applied to primary, secondary and tertiary recovery processes in conventional reservoirs. CRM’s predict well flow rates based solely on previously observed production and injection rates, and producers’ bottomhole pressures (BHP’s); i.e., a geological model and rock/fluid properties are not required. CRM’s can accelerate the learning curve of the geological analysis by providing interwell connectivity maps to corroborate features such as sealing or leaking faults, and high permeability channels. Additionally, oil and water rates are computed by coupling a fractional flow model to CRM’s, which enables, for example, optimization of water allocation in mature fields undergoing waterflooding. In this dissertation, a comprehensive review on CRM’s is presented, summarizing theoretical concepts and relevant aspects for implementation to field data. Additionally, two case studies are presented distinguishing CRM interwell connectivities from streamline allocation factors. For unconventional reservoirs, the second Jacobi theta function (θ2 model) is a physics-based decline curve model proposed, which can be considered an extension of CRM. It accounts for linear flow and material balance in horizontal multi-stage hydraulically fractured wells. The main characteristics of pressure diffusion in the porous media are embedded in the functional form, such that there is a transition from transient to boundary dominated flow and the EUR is always finite. Analogously to the frequently used Arps hyperbolic, the new model has only three parameters, where two of them define the decline profile and the third one is a multiplier. A case study of 992 gas wells in the Barnett shale is presented with probabilistic forecasts of flowrates and estimated ultimate recovery (EUR) performed in a Bayesian approach. New methodologies are proposed for data treatment, uncertainty calibration, and the design of a localized prior distribution for each well. The results indicate that uncertainty is reliably quantified, and the θ2 model has smaller uncertainty and provides more conservative forecasts than other decline models commonly used (Arps hyperbolic, Duong and stretched exponential models). Additionally, the use of previous production of surrounding wells and geospatial data reduces the uncertainty on the performance of new… Advisors/Committee Members: Gildin, Eduardo (advisor), Blasingame, Thomas A. (committee member), Killough, John (committee member), Duffield, Nick (committee member).

Subjects/Keywords: reservoir simulation; material balance; unconventional reservoirs; waterflooding; enhanced oil recovery; automatic decline curve analysis; Jacobi theta functions; capacitance-resistance model; Bayesian estimation; localized prior; legal data

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

APA (6^th Edition):

Wanderley De Holanda, R. (2019). Material Balance Reservoir Models Derived from Production Data. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/185018

Chicago Manual of Style (16^th Edition):

Wanderley De Holanda, Rafael. “Material Balance Reservoir Models Derived from Production Data.” 2019. Doctoral Dissertation, Texas A&M University. Accessed December 12, 2019. http://hdl.handle.net/1969.1/185018.

MLA Handbook (7^th Edition):

Wanderley De Holanda, Rafael. “Material Balance Reservoir Models Derived from Production Data.” 2019. Web. 12 Dec 2019.

Vancouver:

Wanderley De Holanda R. Material Balance Reservoir Models Derived from Production Data. [Internet] [Doctoral dissertation]. Texas A&M University; 2019. [cited 2019 Dec 12]. Available from: http://hdl.handle.net/1969.1/185018.

Council of Science Editors:

Wanderley De Holanda R. Material Balance Reservoir Models Derived from Production Data. [Doctoral Dissertation]. Texas A&M University; 2019. Available from: http://hdl.handle.net/1969.1/185018

28. Arène, Christophe. Géométrie et arithmétique explicites des variétés abéliennes et applications à la cryptographie : African immigrants in the french housing market : segregation,discrimination and mobility.

Degree: Docteur es, Mathématiques, 2011, Aix-Marseille 2

URL: http://www.theses.fr/2011AIX22069

►

Les principaux objets étudiés dans cette thèse sont les équations décrivant le morphisme de groupe sur une variété abélienne, plongée dans un espace projectif, et… (more)

▼

Les principaux objets étudiés dans cette thèse sont les équations décrivant le morphisme de groupe sur une variété abélienne, plongée dans un espace projectif, et leurs applications en cryptographie. Notons g sa dimension et k son corps de définition. Ce mémoire est composé de deux parties. La première porte sur l'étude des courbes d'Edwards, un modèle pour les courbes elliptiques possédant un sous-groupe de points k-rationnels cyclique d'ordre 4, connues en cryptographie pour l'efficacité de leur loi d'addition et la possibilité qu'elle soit définie pour toute paire de points k-rationnels (loi d'addition k-complète). Nous en donnons une interprétation géométrique et en déduisons des formules explicites pour le calcul du couplage de Tate réduit sur courbes d'Edwards tordues, dont l'efficacité rivalise avec les modèles elliptiques couramment utilisés. Cette partie se conclut par la génération, spécifique au calcul de couplages, de courbes d'Edwards dont les tailles correspondent aux standards cryptographiques actuellement en vigueur. Dans la seconde partie nous nous intéressons à la notion de complétude introduite ci-dessus. Cette propriété est cryptographiquement importante car elle permet d'éviter des attaques physiques, comme les attaques par canaux cachés, sur des cryptosystèmes basés sur les courbes elliptiques ou hyperelliptiques. Un précédent travail de Lange et Ruppert, basé sur la cohomologie des fibrés en droite, permet une approche théorique des lois d'addition. Nous présentons trois résultats importants : tout d'abord nous généralisons un résultat de Bosma et Lenstra en démontrant que le morphisme de groupe ne peut être décrit par strictement moins de g+1 lois d'addition sur la clôture algébrique de k. Ensuite nous démontrons que si le groupe de Galois absolu de k est infini, alors toute variété abélienne peut être plongée dans un espace projectif de manière à ce qu'il existe une loi d'addition k-complète. De plus, l'utilisation des variétés abéliennes nous limitant à celles de dimension un ou deux, nous démontrons qu'une telle loi existe pour leur plongement projectif usuel. Finalement, nous développons un algorithme, basé sur la théorie des fonctions thêta, calculant celle-ci dans P¹⁵ sur la jacobienne d'une courbe de genre deux donnée par sa forme de Rosenhain. Il est désormais intégré au package AVIsogenies de Magma.

The main objects we study in this PhD thesis are the equations describing the group morphism on an abelian variety, embedded in a projective space, and their applications in cryptograhy. We denote by g its dimension and k its field of definition. This thesis is built in two parts. The first one is concerned by the study of Edwards curves, a model for elliptic curves having a cyclic subgroup of k-rational points of order 4, known in cryptography for the efficiency of their addition law and the fact that it can be defined for any couple of k-rational points (k-complete addition law). We give the corresponding geometric interpretation and deduce explicit formulae to calculate the reduced…

Advisors/Committee Members: Kohel, David R. (thesis director).

Subjects/Keywords: Courbes d'Edwards tordues; Courbe elliptique; Loi d'addition k-complète; Couplage de Tate réduit; Formules explicites; Fibré en droites; Plongement projectif; Jacobienne d'une courbe de genre 2; Fonctions thêta; Thêta constantes; Twisted Edwards curves; Elliptic curve; K-complete addition law; Reduced Tate pairing; Explicite formulae; Line bundle; Projective embedding; Jacobian of a genus 2 curve; Theta functions; Theta constants

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

APA (6^th Edition):

Arène, C. (2011). Géométrie et arithmétique explicites des variétés abéliennes et applications à la cryptographie : African immigrants in the french housing market : segregation,discrimination and mobility. (Doctoral Dissertation). Aix-Marseille 2. Retrieved from http://www.theses.fr/2011AIX22069

Chicago Manual of Style (16^th Edition):

Arène, Christophe. “Géométrie et arithmétique explicites des variétés abéliennes et applications à la cryptographie : African immigrants in the french housing market : segregation,discrimination and mobility.” 2011. Doctoral Dissertation, Aix-Marseille 2. Accessed December 12, 2019. http://www.theses.fr/2011AIX22069.

MLA Handbook (7^th Edition):

Arène, Christophe. “Géométrie et arithmétique explicites des variétés abéliennes et applications à la cryptographie : African immigrants in the french housing market : segregation,discrimination and mobility.” 2011. Web. 12 Dec 2019.

Vancouver:

Arène C. Géométrie et arithmétique explicites des variétés abéliennes et applications à la cryptographie : African immigrants in the french housing market : segregation,discrimination and mobility. [Internet] [Doctoral dissertation]. Aix-Marseille 2; 2011. [cited 2019 Dec 12]. Available from: http://www.theses.fr/2011AIX22069.

Council of Science Editors:

Arène C. Géométrie et arithmétique explicites des variétés abéliennes et applications à la cryptographie : African immigrants in the french housing market : segregation,discrimination and mobility. [Doctoral Dissertation]. Aix-Marseille 2; 2011. Available from: http://www.theses.fr/2011AIX22069

29. Xu, Ping. Identities involving theta functions and analogues of theta functions.

Degree: PhD, 0439, 2013, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/45365

► My dissertation is mainly about various identities involving theta functions and analogues of theta functions. In Chapter 1, we give a completely elementary proof of… (more)

Subjects/Keywords: Circular summation formula; elementary proof; two-dimensional lattice sums; Poisson equation; theta functions; analogue of theta functions; analogue of Gauss sums

…the most useful theorem in the theory of theta functions that was first discovered by… …which has its combinatorial interpretation in terms of the partitions. Theta functions play a… …To learn how q-series articulate with theta functions and number theory, in particular in… …identities involving theta functions and analogues of theta functions, and applications of theta… …introduce Jacobi theta functions θ2 (z|τ ) and θ3 (z|τ ) ∞ 2 q (n+1/2…

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

APA (6^th Edition):

Xu, P. (2013). Identities involving theta functions and analogues of theta functions. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/45365

Chicago Manual of Style (16^th Edition):

Xu, Ping. “Identities involving theta functions and analogues of theta functions.” 2013. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed December 12, 2019. http://hdl.handle.net/2142/45365.

MLA Handbook (7^th Edition):

Xu, Ping. “Identities involving theta functions and analogues of theta functions.” 2013. Web. 12 Dec 2019.

Vancouver:

Xu P. Identities involving theta functions and analogues of theta functions. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2013. [cited 2019 Dec 12]. Available from: http://hdl.handle.net/2142/45365.

Council of Science Editors:

Xu P. Identities involving theta functions and analogues of theta functions. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2013. Available from: http://hdl.handle.net/2142/45365

30. Labrande, Hugo. Explicit computation of the Abel-Jacobi map and its inverse : Calcul explicite de l'application d'Abel-Jacobi et de son inverse.

Degree: Docteur es, Informatique, 2016, Université de Lorraine; University of Calgary

URL: http://www.theses.fr/2016LORR0142

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L'application d'Abel-Jacobi fait le lien entre la forme de Weierstrass d'une courbe elliptique définie sur C et le tore complexe qui lui est associé. Il… (more)

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L'application d'Abel-Jacobi fait le lien entre la forme de Weierstrass d'une courbe elliptique définie sur C et le tore complexe qui lui est associé. Il est possible de la calculer en un nombre d'opérations quasi-linéaire en la précision voulue, c'est à dire en temps O(M(P) log P). Son inverse est donné par la fonction p de Weierstrass, qui s'exprime en fonction de thêta, une fonction importante en théorie des nombres. L'algorithme naturel d'évaluation de thêta nécessite O(M(P) sqrt(P)) opérations, mais certaines valeurs (les thêta-constantes) peuvent être calculées en O(M(P) log P) opérations en exploitant les liens avec la moyenne arithmético-géométrique (AGM). Dans ce manuscrit, nous généralisons cet algorithme afin de calculer thêta en O(M(P) log P). Nous exhibons une fonction F qui a des propriétés similaires à l'AGM. D'une façon similaire à l'algorithme pour les thêta-constantes, nous pouvons alors utiliser la méthode de Newton pour calculer la valeur de thêta. Nous avons implanté cet algorithme, qui est plus rapide que la méthode naïve pour des précisions supérieures à 300 000 chiffres décimaux. Nous montrons comment généraliser cet algorithme en genre supérieur, et en particulier comment généraliser la fonction F. En genre 2, nous sommes parvenus à prouver que la même méthode mène à un algorithme qui évalue thêta en O(M(P) log P) opérations ; la même complexité s'applique aussi à l'application d'Abel-Jacobi. Cet algorithme est plus rapide que la méthode naïve pour des précisions plus faibles qu'en genre 1, de l'ordre de 3 000 chiffres décimaux. Nous esquissons également des pistes pour obtenir la même complexité en genre quelconque. Enfin, nous exhibons un nouvel algorithme permettant de calculer une isogénie de courbes elliptiques de noyau donné. Cet algorithme utilise l'application d'Abel-Jacobi, car il est facile d'évaluer l'isogénie sur le tore ; il est sans doute possible de le généraliser au genre supérieur

The Abel-Jacobi map links the short Weierstrass form of a complex elliptic curve to the complex torus associated to it. One can compute it with a number of operations which is quasi-linear in the target precision, i.e. in time O(M(P) log P). Its inverse is given by Weierstrass's p-function, which can be written as a function of theta, an important function in number theory. The natural algorithm for evaluating theta requires O(M(P) sqrt(P)) operations, but some values (the theta-constants) can be computed in O(M(P) log P) operations by exploiting the links with the arithmetico-geometric mean (AGM). In this manuscript, we generalize this algorithm in order to compute theta in O(M(P) log P). We give a function F which has similar properties to the AGM. As with the algorithm for theta-constants, we can then use Newton's method to compute the value of theta. We implemented this algorithm, which is faster than the naive method for precisions larger than 300,000 decimal digits. We then study the generalization of this algorithm in higher genus, and in particular how to generalize the F function. In…

Advisors/Committee Members: Thomé, Emmanuel (thesis director), Jacobson, Michael J. (thesis director).

Subjects/Keywords: Fonctions thêta; Application d'Abel-Jacobi; Multiprécision; Temps quasi-Linéaire; Courbes elliptiques; Isogénies; Courbes hyperelliptiques; Cryptographie; Theta functions; Abel-Jacobi map; Multiprecision; Quasi-Linear time; Elliptic curves; Isogenies; Hyperelliptic curves; Cryptography; 005.82

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APA (6^th Edition):

Labrande, H. (2016). Explicit computation of the Abel-Jacobi map and its inverse : Calcul explicite de l'application d'Abel-Jacobi et de son inverse. (Doctoral Dissertation). Université de Lorraine; University of Calgary. Retrieved from http://www.theses.fr/2016LORR0142

Chicago Manual of Style (16^th Edition):

Labrande, Hugo. “Explicit computation of the Abel-Jacobi map and its inverse : Calcul explicite de l'application d'Abel-Jacobi et de son inverse.” 2016. Doctoral Dissertation, Université de Lorraine; University of Calgary. Accessed December 12, 2019. http://www.theses.fr/2016LORR0142.

MLA Handbook (7^th Edition):

Labrande, Hugo. “Explicit computation of the Abel-Jacobi map and its inverse : Calcul explicite de l'application d'Abel-Jacobi et de son inverse.” 2016. Web. 12 Dec 2019.

Vancouver:

Labrande H. Explicit computation of the Abel-Jacobi map and its inverse : Calcul explicite de l'application d'Abel-Jacobi et de son inverse. [Internet] [Doctoral dissertation]. Université de Lorraine; University of Calgary; 2016. [cited 2019 Dec 12]. Available from: http://www.theses.fr/2016LORR0142.

Council of Science Editors:

Labrande H. Explicit computation of the Abel-Jacobi map and its inverse : Calcul explicite de l'application d'Abel-Jacobi et de son inverse. [Doctoral Dissertation]. Université de Lorraine; University of Calgary; 2016. Available from: http://www.theses.fr/2016LORR0142

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