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Über spezielle rekurrente Folgen und ihre Bedeutung für die Theorie der linearen Mittelbildungen und KettenbrücheVerbeek, Maria, January 1917 (has links)
Thesis (doctoral)Rheinische FriedrichWilhelmsUniversität zu Bonn, 1917. / Vita. Includes bibliographical references.

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Fully sequential monitoring of longitudinal trials using sequential ranks, with applications to an orthodontics studyBogowicz, Paul Joseph. January 2009 (has links)
Thesis (M. Sc.)University of Alberta, 2009. / Title from pdf file main screen (viewed on Aug. 27, 2009). "A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Master of Science in Statistics, Department of Mathematical and Statistical Sciences, University of Alberta." Includes bibliographical references.

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Langford sequences and their variants: partitions of {1, . . . , 2m + 2} \ {k, 2m + 1}, {1, . . . , 2m?1, L} and {1, . . . , 2m, L} \ {2} into differences in {d, . . . , d + m ?1} /Mor, S.J. January 1900 (has links)
Thesis (M.Sc.)  Carleton University, 2007. / Includes bibliographical references (p. 7075). Also available in electronic format on the Internet.

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Escher's problem and numerical sequencesPalmacci, Matthew Stephen. January 2006 (has links)
Thesis (M.S.)Worcester Polytechnic Institute. / Keywords: sequences, Escher, Catalan, Collatz, integer. Includes bibliographical references (p.2728).

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College students' intuitive understanding of the concept of limit and their level of reverse thinkingRoh, Kyeong Hah, January 2005 (has links)
Thesis (Ph. D.)Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains xiv, 260 p.; also includes graphics (some col.). Includes bibliographical references (p. 210217). Available online via OhioLINK's ETD Center

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Congruence properties of linear recurring sequencesCrouch, Nicholas Errol January 2006 (has links)
This thesis deals with the behaviour modulo n of linear recurring sequences of integers with characteristic polynomial ƒ ( x ) where n is a positive integer and ƒ ( x ) is a monic polynomial of degree k. Let α [subscript 1], α [subscript 2],...,α [subscript k] be the zeros of ƒ ( x ) and D ( ƒ ) ≠ 0 its discriminant. We focus on the vsequence ( v [subscript j] ), defined by v [subscript j] = α[superscript j] over [subscript 1] + α [superscript j] over [subscript 2] + ... + α [superscript j] over [subscript k] for j ≥ 0. Our main interest is in algebraic congruences modulo n which hold when n is a prime and which involve only terms of the sequence and rational integers. For k = 1,2 such results have been used extensively in primality testing and have led to the study of various types of pseudoprimes. For k = 3, such results have been studied by Adams and Shanks ( 1 ) under the further assumption ƒ ( 0 ) =  1. For general k, quite different approaches have been taken by Gurak ( 2 ) and Szekeres ( 3 ). The infinite test matrix modulo n is the infinite matrix M with rows and columns numbered 0,1,2 ... whose ( i, j ) entry is m [subscript ij], the least residue modulo n of v [subscript in + j]  v [subscript i + j] for i ≥ 0 and j ≥ 0. We study the congruence properties of M and especially of the k x k submatrix M ( [superscript k] ) determined by rows and columns 0 to k  1. Chapters 1 and 2 introduce the thesis and summarise auxiliary results. Chapter 3 presents background on linear recurring sequences with an emphasis on the matrix approach, including the v  sequence and the k " u  sequences " ( whose initial vectors are the rows of Ik ). Chapter 4 comprises theoretical study of the properties of M for a general k, both when n is a prime and for general n, together with investigation of the condition of Gurak ( 2 ). For ( n, k!D ( ƒ ) ) = 1, we show that the condition of Szekeres is equivalent to the condition that m [subscript i0] = 0 for 1 ≤ i ≤ k and also to certain permutation conditions. Gurak ' s condition is then described using these conditions. Chapter 5 assumes k = 3. For this case we study congruences modulo n satisfied by the m [subscript ij] when n is a prime, and hence develop a combination of tests on M ( [superscript 3] ) which are passed by all primes. We report on extensive computer investigation of composites passing these tests. Such composites are found to be rare. Investigation of the relevant work of Adams and Shanks and colleagues, together with use of the permutation condition of Chapter 4, leads to a modification of the earlier tests on M ( [superscript 3] ). Under suitable assumptions we show that the new modified condition is equivalent to the basic condition of Adams and Shanks and also to that of Gurak but has significant advantages over both. References ( 1 ) Adams, W. and Shanks, D. Strong primality tests that are not sufficient, Math. Comp., 39, 1982, 255300. ( 2 ) Gurak, S. Pseudoprimes for higher  order linear recurrence sequences, Math. Comp., 55, 1990, 783813. ( 3 ) Szekeres, G., Higher order pseudoprimes in primality testing, pp 451458, in Combinatorics, Paul Erdos is eighty, Vol. 2 ( Jesztgektm 1993 ), Bolyai Soc. Math. Stud., 2, Jnos Bolyai Math. Soc. Budapest, 1996. / Thesis (M.Sc.)School of Mathematical Sciences, 2006.

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Contrasting sequence groups by emerging sequencesDeng, Kang. January 2009 (has links)
Thesis (M. Sc.)University of Alberta, 2009. / Title from PDF file main screen (viewed on Nov. 27, 2009). "A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Master of Science, Department of Computing Science, University of Alberta." Includes bibliographical references.

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Suites aléatoires et complexitéJanvier, Claude January 1969 (has links)
No description available.

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Congruence properties of linear recurring sequencesCrouch, Nicholas Errol January 2006 (has links)
This thesis deals with the behaviour modulo n of linear recurring sequences of integers with characteristic polynomial ƒ ( x ) where n is a positive integer and ƒ ( x ) is a monic polynomial of degree k. Let α [subscript 1], α [subscript 2],...,α [subscript k] be the zeros of ƒ ( x ) and D ( ƒ ) ≠ 0 its discriminant. We focus on the vsequence ( v [subscript j] ), defined by v [subscript j] = α[superscript j] over [subscript 1] + α [superscript j] over [subscript 2] + ... + α [superscript j] over [subscript k] for j ≥ 0. Our main interest is in algebraic congruences modulo n which hold when n is a prime and which involve only terms of the sequence and rational integers. For k = 1,2 such results have been used extensively in primality testing and have led to the study of various types of pseudoprimes. For k = 3, such results have been studied by Adams and Shanks ( 1 ) under the further assumption ƒ ( 0 ) =  1. For general k, quite different approaches have been taken by Gurak ( 2 ) and Szekeres ( 3 ). The infinite test matrix modulo n is the infinite matrix M with rows and columns numbered 0,1,2 ... whose ( i, j ) entry is m [subscript ij], the least residue modulo n of v [subscript in + j]  v [subscript i + j] for i ≥ 0 and j ≥ 0. We study the congruence properties of M and especially of the k x k submatrix M ( [superscript k] ) determined by rows and columns 0 to k  1. Chapters 1 and 2 introduce the thesis and summarise auxiliary results. Chapter 3 presents background on linear recurring sequences with an emphasis on the matrix approach, including the v  sequence and the k " u  sequences " ( whose initial vectors are the rows of Ik ). Chapter 4 comprises theoretical study of the properties of M for a general k, both when n is a prime and for general n, together with investigation of the condition of Gurak ( 2 ). For ( n, k!D ( ƒ ) ) = 1, we show that the condition of Szekeres is equivalent to the condition that m [subscript i0] = 0 for 1 ≤ i ≤ k and also to certain permutation conditions. Gurak ' s condition is then described using these conditions. Chapter 5 assumes k = 3. For this case we study congruences modulo n satisfied by the m [subscript ij] when n is a prime, and hence develop a combination of tests on M ( [superscript 3] ) which are passed by all primes. We report on extensive computer investigation of composites passing these tests. Such composites are found to be rare. Investigation of the relevant work of Adams and Shanks and colleagues, together with use of the permutation condition of Chapter 4, leads to a modification of the earlier tests on M ( [superscript 3] ). Under suitable assumptions we show that the new modified condition is equivalent to the basic condition of Adams and Shanks and also to that of Gurak but has significant advantages over both. References ( 1 ) Adams, W. and Shanks, D. Strong primality tests that are not sufficient, Math. Comp., 39, 1982, 255300. ( 2 ) Gurak, S. Pseudoprimes for higher  order linear recurrence sequences, Math. Comp., 55, 1990, 783813. ( 3 ) Szekeres, G., Higher order pseudoprimes in primality testing, pp 451458, in Combinatorics, Paul Erdos is eighty, Vol. 2 ( Jesztgektm 1993 ), Bolyai Soc. Math. Stud., 2, Jnos Bolyai Math. Soc. Budapest, 1996. / Thesis (M.Sc.)School of Mathematical Sciences, 2006.

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Genetic algorithm using restricted sequence alignmentsLiakhovitch, Evgueni. January 2000 (has links)
Thesis (M.S.)Ohio University, August, 2000. / Title from PDF t.p.

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