Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 20 of 255 for “"Integers"”.
-
The Factoradic Integers
… examined; this leads to the consideration of the integers as a metric space under the "factoradic metric", i.e., the integers equipped with a distance function defined by d(n,m)=1/N!, where N is the largest positive integer such that N! divides n-m. Via the process of metric completion, the …
-
Covering Sets of the Integers
Made available in DSpace on 2014-12-11T18:23:43Z (GMT). No. of bitstreams: 1 7121162.pdf: 3349128 bytes, checksum: ff4e647d59c04f1ac0287e0172b96651 (MD5) Previous issue date: 1971
-
Arithmetic Structure in Sets of Integers
… arithmetic structures in dense sets of integers. In Chapter 1 we give an exposition of the state-of-the-art technique due to Pintz, Steiger and Szemer edi which yields the best known upper bound on the density of sets whose di erence set is square-free. Inspired by the well-known fact …
-
A Discrete Pareto Distribution on Positive Integers
The Zipf's law is a standard discrete power-law probability distributions, often thought of as a discrete counterpart of the Pareto distribution. Here we study an alternative discrete Pareto distribution, using the general approach of discretizing a continuous distribution. We obtain several …
-
Generalized and restricted multiplication tables of integers
Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-06-11T20:10:14Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 Koukoulopoulos_Dimitrios.tex: 150989 bytes, checksum: 0478d1ce3b482241f0d7d6d6daf5dde5 (MD5) Koukoulopoulos_Dimitrios.pdf: …
-
Quadratic Forms Representing All Integers Coprime to 3
… integer-valued quadratic forms representing odd integers, we show that an integer-valued quadratic form representing all positive integers coprime to 3 up to 290 must represent all positive integers coprime to 3. We further this result by enumerating a list of 31 critical numbers such that …
-
Ideal Membership in Polynomial Rings Over the Integers
… with coefficients in the ring Z p of p-adic integers. We also consider the ideal membership problem for ideals of the ring Z p⟨X⟩ itself, and for ideals of its subring Z p⟨X⟩alg consisting of the restricted p-adic power series which are algebraic over Z [X]. Here, we make …
-
Group Representations Over Integers Modulo a Prime Power
Made available in DSpace on 2014-12-09T22:17:38Z (GMT). No. of bitstreams: 1 6801764.pdf: 1448098 bytes, checksum: 62f175e854b32519095eb27773c884de (MD5) Previous issue date: 1967
-
On subset-sum-distinct sequences of positive integers
"An SSD-sequence of integers is one in which each subset is uniquely determined by its sum. Such sequences are ""sparse"". Ryavec used a generating function technique to show that the sum of the reciprocals of the terms of such a sequence is at most two, and that the greedy algorithm generates the …
-
Combinatorial Problems on the Integers: Colorings, Games, and Permutations
… of several combinatorial problems on the integers. These problems fit inside the areas of extremal combinatorics and enumerative combinatorics.</p> <p>We first study monochromatic solutions to equations when integers are colored with finitely many colors in Chapter 2. By looking at subsets …
-
Asymptotic Distribution of Beurling's Generalized Prime Numbers and Integers
… generalized (henceforth g-) prime numbers and integers Acta Math. 1937 . We call P = p(,i) (,i=1)('(INFIN)), where 1 ) (INFIN), a set of g-primes. The set of all products of g-primes is called the associated set of g-integers. Define summatory functions N(x), (psi)(x), (PI)(x) and M(x).
-
Localization of Divisors of Integers and of Some Arithmetic Functions
… related to the multiplicative structure of integers. First, we determine the order of magnitude of the function H2(x, y, z), the number of positive integers n ≤ x having exactly two divisors in ( y, z], in the range of y10 ≤ z ≤ x1/3, and that of the function H3(x, y, z), the number …
-
Iterates of functions defined in terms of digital representations of the integers
For a fixed base, John H. Conway’s RATS sequences are generated by iterating the following procedure on an initial integer: Reverse the digits of the integer, Add the reversal to the original, Then Sort the resulting digits in increasing order. For example, 334+433=767, which gets sorted into 677. …
-
Multiple gamma functions and derivatives of L-functions at non-positive integers
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996.
-
Searching in a Sorted Linked List and Sort Integers into a Linked List
… processors based on the trie with all the given integers. Additional nodes (O(nloglogm) of them) are added to the tree. After the tree is constructed, for any given integer we can find the predecessor and successor of the integer, insert or delete the integer in O(loglogm) time. The result …
-
Exact covering system digraphs a number-theoretic family of directed graphs on the integers
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-11 without embargo terms
-
The distribution of k-free numbers and integers with fixed number of prime factors
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-09-29 without embargo terms
-
Sums of Multiplicative Functions Over Integers Without Large Prime Factors and Related Differential Difference Equations
Integers without large prime factors arise naturally in various areas of number theory. Counting functions of such integers have been the subject of numerous past studies. Traditionally, Psi(x, y) denotes the number of positive integers up to x, all of whose prime divisors are less than or equal to …
-
Security systems based on Gaussian integers : Analysis of basic operations and time complexity of secret transformations
… arithmetic modulo prime numbers. Gaussian integers can be used with most security algorithms that are formulated for real integers. The aim of this work is to study the benefits of common security protocols with Gaussian integers. Although the main contribution of this work is to analyze …
Page 1 of 13