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You searched for subject:(Collatz Conjecture). Showing records 1 – 3 of 3 total matches.

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1. Ibrahim Ahmed, Abdoulkarim. Monogénéité et systèmes de numération : Monogeneity and system numeration.

Degree: Docteur es, Mathematiques, 2016, Besançon

Cette thèse est centrée autour de la monogénéité de corps de nombres en situation relative puis à la conjecture de Collatz.\newline Premièrement on détermine l'ensemble de classes des générateurs de l'anneau des entiers des certaines extensions relatives de corps de nombres, en utilisant l'algorithme de Gaál & Phost et le logiciel PARI/GP. La deuxième partie propose différents formulations d'une généralisation de la conjecture de Collatz, aux entiers p-adiques. On étudie ensuite le comportement de suites analogues dans le cadre d'anneaux d'entiers de corps de nombres.

This thesis are centered around the monogeneity of number fields in a relative situation and the Collatz conjecture. Firstly, we determine the set of generator classes of the ring of integers of some relative extensions of number fields, using the Gaál& Phost algorithm and the PARI/GP software. The second part proposes different formulations of a generalization of the Collatz conjecture to p-adic integers. We then study the behavior of similar sequences in the framework of rings of integers of number fields.

Advisors/Committee Members: Fleckinger, Vincent (thesis director).

Subjects/Keywords: Anneaux des entiers; Monogénéité; Extensions relatives; Équation de Thue; Conjecture de Collatz; Ring of integers; Monogeneity; Relative extension; Thue equation; Conjecture of Collatz; 512; 11B37; 11D45; 11D59; 11B83; 26A18

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APA (6th Edition):

Ibrahim Ahmed, A. (2016). Monogénéité et systèmes de numération : Monogeneity and system numeration. (Doctoral Dissertation). Besançon. Retrieved from http://www.theses.fr/2016BESA2039

Chicago Manual of Style (16th Edition):

Ibrahim Ahmed, Abdoulkarim. “Monogénéité et systèmes de numération : Monogeneity and system numeration.” 2016. Doctoral Dissertation, Besançon. Accessed December 06, 2019. http://www.theses.fr/2016BESA2039.

MLA Handbook (7th Edition):

Ibrahim Ahmed, Abdoulkarim. “Monogénéité et systèmes de numération : Monogeneity and system numeration.” 2016. Web. 06 Dec 2019.

Vancouver:

Ibrahim Ahmed A. Monogénéité et systèmes de numération : Monogeneity and system numeration. [Internet] [Doctoral dissertation]. Besançon; 2016. [cited 2019 Dec 06]. Available from: http://www.theses.fr/2016BESA2039.

Council of Science Editors:

Ibrahim Ahmed A. Monogénéité et systèmes de numération : Monogeneity and system numeration. [Doctoral Dissertation]. Besançon; 2016. Available from: http://www.theses.fr/2016BESA2039


University of Texas – Austin

2. -7002-7426. Challenging variants of the Collatz Conjecture.

Degree: MSin Computer Science, Computer science, 2018, University of Texas – Austin

The Collatz Conjecture (also known as the 3N + 1 problem) is simple to explain, yet proving that all positive integers following the Collatz Mapping must converge to 1 has eluded mathematicians for over half a century. Aaronson and Heule are exploring solving the Collatz Conjecture using an approach involving string rewrite systems: Aaronson transformed the Conjecture into a string rewrite system and Heule has been applying parallel SAT solvers on instances of this system. Similar approaches have been applied successfully to other mathematical problems. We started looking into simpler variants of the conjecture. This thesis defines some of these variants and investigates easily provable as well as very hard variants. We study the hardness of unsolved variants by computing the number of rewrite steps needed up to 1 billion. Our hardness prediction method suggests that proving termination of the challenging variants should be considerably easier compared to solving the original conjecture. Advisors/Committee Members: Aaronson, Scott (advisor), Heule, Marijn, 1979- (advisor).

Subjects/Keywords: Collatz Conjecture; 3X + 1 problem; String rewrite systems; SAT solving; Matrix interpretation

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APA (6th Edition):

-7002-7426. (2018). Challenging variants of the Collatz Conjecture. (Masters Thesis). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/1559

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Chicago Manual of Style (16th Edition):

-7002-7426. “Challenging variants of the Collatz Conjecture.” 2018. Masters Thesis, University of Texas – Austin. Accessed December 06, 2019. http://dx.doi.org/10.26153/tsw/1559.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7th Edition):

-7002-7426. “Challenging variants of the Collatz Conjecture.” 2018. Web. 06 Dec 2019.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-7002-7426. Challenging variants of the Collatz Conjecture. [Internet] [Masters thesis]. University of Texas – Austin; 2018. [cited 2019 Dec 06]. Available from: http://dx.doi.org/10.26153/tsw/1559.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-7002-7426. Challenging variants of the Collatz Conjecture. [Masters Thesis]. University of Texas – Austin; 2018. Available from: http://dx.doi.org/10.26153/tsw/1559

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete


University of Akron

3. Stroup, David A. Collatz’s Problem and Encoding Vectors.

Degree: MS, Mathematics, 2006, University of Akron

The first chapter introduces the Collatz conjecture. The second chapter presents a brief literature survey. The third chapter presents some theorems and conjectures regarding encoding vectors for various moduli. Appendices include a presentation of numerical data, which serves as a concrete illustration of the findings in chapter 3, and a Java program for independent analysis of the Collatz conjecture. Advisors/Committee Members: Norfolk, T. (Advisor).

Subjects/Keywords: Mathematics; Collatz conjecture; 3x+1 problem; Syracuse problem; Ulam Conjecture; hailstone numbers; Hasse algorithm

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

APA (6th Edition):

Stroup, D. A. (2006). Collatz’s Problem and Encoding Vectors. (Masters Thesis). University of Akron. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=akron1145048595

Chicago Manual of Style (16th Edition):

Stroup, David A. “Collatz’s Problem and Encoding Vectors.” 2006. Masters Thesis, University of Akron. Accessed December 06, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=akron1145048595.

MLA Handbook (7th Edition):

Stroup, David A. “Collatz’s Problem and Encoding Vectors.” 2006. Web. 06 Dec 2019.

Vancouver:

Stroup DA. Collatz’s Problem and Encoding Vectors. [Internet] [Masters thesis]. University of Akron; 2006. [cited 2019 Dec 06]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=akron1145048595.

Council of Science Editors:

Stroup DA. Collatz’s Problem and Encoding Vectors. [Masters Thesis]. University of Akron; 2006. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=akron1145048595

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